{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1eY-Qmf8ItWv"
      },
      "source": [
        "# Autoencoders"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yEqo3q8JI5uG"
      },
      "source": [
        "When training CNNs, one of the problems is that we need a lot of labeled data. In the case of image classification, we need to separate images into different classes, which is a manual effort.\n",
        "\n",
        "However, we might want to use raw (unlabeled) data for training CNN feature extractors, which is called **self-supervised learning**. Instead of labels, we will use training images as both network input and output. The main idea of **autoencoder** is that we will have an **encoder network** that converts input image into some **latent space** (normally it is just a vector of some smaller size), then the **decoder network**, whose goal would be to reconstruct the original image.\n",
        "\n",
        "Since we are training autoencoder to capture as much of the information from the original image as possible for accurate reconstruction, the network tries to find the best **embedding** of input images to capture the meaning.\n",
        "\n",
        "![AutoEncoder Diagram](images/autoencoder_schema.jpg)\n",
        "\n",
        "*Image from [Keras blog](https://blog.keras.io/building-autoencoders-in-keras.html)*\n",
        "\n",
        "Most of the examples below are inspired by [this article](https://blog.keras.io/building-autoencoders-in-keras.html)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UZ38ZCGRYhHh"
      },
      "source": [
        "Let's create simplest autoencoder for MNIST:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "48ua_UfDIqum",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "import tensorflow as tf\n",
        "from tensorflow.keras.datasets import mnist\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "(x_train, y_trainclass), (x_test, y_testclass) = mnist.load_data()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 109
        },
        "id": "-VvA6_e_Ytv9",
        "outputId": "7f43ddd9-2044-4c88-a57d-7dffbb0741fe",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "data": {
            "image/png": 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+08/z5Vv43iu78c1odI1YGLNVZLEEjgPtrZjtYYJtZW6PjZFUK7ioFN06RVdybjZJ7CwYmdqVG3KdNJWR26NjaOcmSISCtIRDyHodt1QmOHMT/++mBxnqmeH2wX/geL2Hmee7SI1ImM3g1hYElM75iSMtJxvRu2s3Zw7v51EScazNHUw+YPAnv/olBrQsmzQVdaFjc9IR/NXM29h/ro9tX6ijzaYp7G6nFlc4/bMBTuoDdD9lsW14vlEkq1hECAWfqpL7yC4c6XK/f4ZbOh7n6a2DmENd+CbzsFpGrqjQ3UGtI0x3Ypatep6Qtvrm6erQapTO99OMpeN0HbEIjDengV0NIhQis0tgDOZ5OPo62/RGJG5JhyfK29mX20zrqxD44Ss4zZRKWYLb28HMfTHye0x+/PY/JakoBBWdY3WXL83ez/NnNzP0lxXUiTROJou0LRwpUUIh8jclKPSrfHDwRf5l8tD5wQTjtsY5O4F6Kkj7TyeQ2dyKXSNNZeRICdJBVquNKNqykPU6St3FNTUqlg9HSiJqlVqbjVbRELp+8T4AaW2MCEoYBkrAj9OTIjsUoNZlMaBliSkOFeliuZKiFBw2ezg43Y0zFUTNZ5CFIoHpGFpZR7F1XBX8UyXI5nGrtTe0BpCNSR5+oeIqDm2JItlt7SREDPXU6kyEEapKPRWi3Kkz4C/jFwJ9FSNyofsaOgdcuo0cQcUEVBxbRS/bYG6M6+nnEYaBDAVwu2rc3jlGSi0DOhVZp+g6PJUe4vC5LnrnnbWbJHYDaB3tOD0pMrsi5G612NE/Rauqkncdnii38ExxG88cHiJwTkfNjOMWS0jbOn/NC12j2KdS2mKzyZg7b+KOlDxeupkn57YRnJbIYgm5gh2/zWXkC0jbRhaL518Ly0FUDcp1Hw6wVc/w0O3HeC65CflYGKY37qw7JR5DdrQwd1uY8jtLPNA7So8GlhSM2jo5N8DRWg9Pz2+F/TFS4y7MzeNk5lH25zGEgl9tPCa7deuy1R0NoaMLlUd6DvHXv3AvdjBKx9MKyJU3VKFr5AYN8oPw/sgEMcWHJlbPyJVYBBGNIBJ17g6eoUs1gSBuVUOfzUFx4w07FJqGEo9htUf5yM0v8a9bXsQQGpZ0SDsOY3aUwy9von0/BE/PNeUTSWV3H2MPa3TcMsPTO79CUAj8wsdPau384cFHcIfDbP+7LMpcDmcufdGXlQiFsO8t8Nvbn2dv4CyLo8IsHL7w2v3Efuan7eViYyLQCnpQUxr5z6OW64TGIqSNGEe2txBUTHaGJxlpSWK1JdFzKdzMfFNGDJdFCGQqSW5njOImuLljmpvCU7hSctry85XMfUxXI5yZb6WQCdE6I/FnHag3IopFPeQ1BgoxtUoyXCHnX8VSWkJgBwVOxCGiNlJlRdtPtWIQs1f4S1pRcfs7qHaFSCZyJNUKloRZp4KoK415Bk2aUrgkQqAEAijRCOXb+shv0tlkzBFWDFxcatJmX62f1yq9BGYUQlNVRLm61q2+JtRUClIJclt0/Fvy3N46RqvioyQtDtXhyfwO3NNhwudAmcvhFopv/I0XZ00n4zgdCVojZQaNaYILne8vmSpn6p2IcT+RcRslV8ZZ4UByQxi5PDNK39+VKNzVw+e2PszdyRE+Gt9Pu5bnM7s/RCLUT+BFCyebXeumLhtC0xCaRuaOBNYHsry7+wz/pu1JAHIu/HX6fl786m0E5lw6T5XoqpfABWHWG6mTG6Bbn2coPsuzoXaEIlanhpiiYCYh0FGiXc8BcCbfipjw4yusbD+H0DUmHo5R213h05tfYEhXOVRXOW52oucUqFSRGyi1Inw+RFc7lS0t5H+ryAPdZ3goeBoacxMpug6fPfUwmTNJtuyrou47im01V5BUuXOAqXs1UndO83c7v4IOmFJhXy3F30zdx8HDm9n+5TmYz2Nn5t8oWy0EimEgIhEqe/op9Gq8q+11bjdmiSsaNWnzH4Z/heHTHfQ/ZRN48vCqjKXfEEbu1i3I5vDPpjh+rgPT0fi1+H7atCKlPglCRy/2o2VTiKoJlo2bXtIJ2oQIw0CJhDGTgtvbJ7g1NEZKNThWd3mscBvPjm0mOebgnzNRJ9JI10X4fGDbN1y9UUViqDarXV5DKhJVdc8PgyzWDPSCQDWXMRpW1MYwtGgY4fMh4xGciJ9yr8POrhkGfHNoqBw32/hJdie+vGiY+AaKyIXPh5MMU2vR2NE6w92RYSKKwMVl0jYZtaOkp2KExxW0bBXXNNe6yVfPwjDDaouG1WdyU3KKTjVA2qlywjJ4pjjEq6f7CY+qkMniFksNE1808FAQZ0s39YRBZqdOtd1lkzGHTwjGbJc5N8jIVAuhEQ1/urhqHrMhjBzXwa1U0I+PseVLfaRv6eHAb/ey05jid375+5yppfj+3p1YuTiBMQ0jB50/MuDU8Fq3/LoRnW3U+pIUhmz+U9cPCAoB+PgfMw/zyld20TpmE3r2JLJaxV6ICBrRs2zaRTGW4khJLh2m44yLnq4sT35WCNRwCBEKUtrTRyWlkt7jEOoo8y+HHucXQ0fpUMHF4M/PPkjhZ+20v2Li5HLLcfR1gxKNMLs7THEz/Nu2A9zvnyGi+Ki4Fl/L72Hf/CY6nlRJ7J9CzqTXurnXhBIIIIIBsjvgP9/zGNt9U7gIDpht/M3UfRx6aQs7/2waWSjizOfO3yuKYSD6uqluSjD1CZObO0f439sPMKCn2bwweuovM2/jpbk+Uo8btDw7jpvJrtrMi41h5NDI+Vaq6JN5QikfT+a3U4vqbDZmSGkFznUlmIpFmdYS1LM6yd4E/kpXI/dVrTbdslRuIkyxz4eRLNGuGtSkzYxjMlxsITZq4Z+s4OQLF5j2jQTiCgIXeX6GKLDqEflFuALFAdxLn5jQtMZTyOJrn44IBBoLjmjq+WqFUlOR4QBSV7GCGnZAI7dFw0xKAm0V+hJZBnxpUqokuDAJJlcKEpqT6IV6U103l0NoGko4hNsao9wtsDtMOtQ8QaEz75jMODrPzA1yejJF/6wFmRyy1kTROICqIjQNxy+5yTdJUrUAg+F6G0cmughOK7gzcwBo7Snw6cigHzdkUOoNUepW2d09zEOJE+z1TyyUvmjMij5dTDE1F6M34zRMvLp6/QYbx8gBt1pFjIwTc1z2fe02ftp3K//uPd/iTv8ot/Y9BkB+yGDCTvC7kQ8TOTVA+/4qvrOzuNkcbrl5Rh7M3Bkh+YFxPtxxBAWFI3WD7+TuYPREB9v3DyOLxeVbxUiAKhSQ7oKZr48pVMJwqIc1pHHp2odKSxK3t63RKSzAbPWT3aZjB8CKSaQCriZxww7v2HWMnkAWQ9iowkUXDg6Cl/P9FOp+aq5ORUp0aaOjUssE6DlRQ5vN01zZ4TdHaUlSumeA3KDGB97/LPeETzOo18i7km8Wb2ZfbjOZb/Sy5fUK2slzFwUKzYBQFdB13IDLJt1FXxhl8g9jt9P9NzrGfLExUqcvxcS9IcwWiW9nntZwkXe2vUKnL8dDwVPEFQgvKQNddiWvH+slcUglOJrBKZVW9Qt+Qxk5UiKtOrJQJDZqAxovFLagC4c7/eeIK7BZd9msT9HakyNjJQhPGKjVBKptI01z3UfmwjAQPh9mEu5tPcuQfxKAOSfKsUIHel5BFlc2N1eTOiXbxyqO/juPlAJn4VEgGDaptvmpdocIFQYueq/VEaPUF0AKkAqYCYXSgIvrd9FjJooiUYBoqMYD8ZP06hlqUseSGmP1Fop2iLFinHwlwFxbFEuCKyWucBGmglaoQbNFpJdiIW9MLEKhX6Pc63Jf5CS3+tL4RaMDb8JMMFmKEZpy0EfncBZzx82K4IIa6qqQuLpCPWGghDsodfsoDTgorSZv7z3FgD/DO0LHiCgWraqKjoq68ERnSYeKVNGzKqFZtzGCZ5U9ZGMZ+QJuLk/4mdOEj8R4bfZWXui8jdQvj3Nv61l+I/ECPZrBX9z0VcaGkvxh1yPMDkfpejZI5BUdN5fHXTJGfb0hhjZR6Y9ibq/yofgBkooNBHihNMixg/0kzoJ0ljliluAsROMAJ8xODoz3Y2TEqq6WpFiCel3Dkhq6UPlvu/6RQ4P9vJTrYzSfuOj9m+ITvC95CkW4qLj4FYu4WgGgLlXm7TAHCpvI1gN87uTbqdR8WBMhtJIgOgxGwSU4YxIEvvYHd7J3xymCoo4iBL68gFOjOPXmH62iBAIo7Skyd6Z47//6DPeGT3G3kSEofOhCxZI2J4rtTKbjbEnXcGbTjUkxTYh0XIRloVQUTlgKKbVOu2rwuW3f4Ik/3oGDwHI1YlqFAd8cEaVGt1qiLhXm3CA5O8C0Y+MXNoN64+lszHZ5vd7ZWJz9Z6dx8qvvHxvSyKVtNya8lCvEgwZGLsLZXY1yp7cFR3GYYlBXGNLTfKtrjP1OP6UzYQKdCTTbXtdG7oQMagmVULhIl+qgCxVTWsyaEfyzCkbeWbY1RZVgEBEMIPSGiZvSoiIdzlZT1NIBwsVVjDpcF60C1bzB6Vo75/yjdKs28fAx2vU852IXFwjd4Z/kHcFx6lJSkQJLKhRdH2XpY9qOU3ENMmaIuWqI7GQMtagSOScw8pLE0SJqpgjVGhg+ymYElcZ6pqZ0UeoCt1JZvfNfQYRh4LRGqaYUPhh7iZt8Go0FVhpYCKaKUZy8jlKt4TbzrGjXRdo2WkVwoLqJnf4JWpU6O3wKN/lOnR8nb0mXoiuxEGRcg5wT5EitF4AeX4a4UqFfy6EKwYwT5qzZhlFwcNZo4e0NaeSLuKaJcnaC4EyALaVuzJYO/vC2X8PssPhPD36bfx6Z4nc7f8RkKsZnW9/Jyb3tdH+nn+C31m/1NqkKHB8YmtPohHLrpB2dF8f76Xq+hm+qcMP1LhY7CUvvvoX5IZU9W04A8GwtxpPFHfzwhVvZ+k0TbSaPs0qP1261Ru+3J3FaInx96iH+dutd9Kay9Iaz1BydunPxpXxKa+NJfTvHsh2MnU2hlhSMjIKvCNERG8Vy0WoOIVuyvVxqzBCu1MCykYUiUhFU9m6j2KNxV+dhNukuZy2dCSeGugEyKovI/k7OPhJGDpaIKRYuFy7WMWZHqT7bSt/rNmJ6bYxquXCrNYRp0vNEnf9v/hHc+/P8w+1fIK64tKoB5hyTI/UWXqkM8O1zt5LJhAm/5kerSHwFSS2p0PWBEfa2DLPd9xI1afO5iYc5MtFFf2btvuA2tJEjZSO6LpXQ6xa+cAjb6KGU1zl7TxtEptih6wzpJUY6DvKsfyvHUjsIadr6zZULgVRAU1xUIbAk5NwAtbIP33gW8jfeySICAZRQkGKPSmWwzrbwLC4uI/VWDs73EJxU0Y6OrmqvPK6DPTyCGPMR33Y7OYKMmCr5Fv8VP5qdjhI9puErSCITdXzzNTh08oJ6O5d6hlH8fqotGpUuQU8gS1gY5FyNYbMdpYmD0vMI0VjMOmZg9ZpsTc2jCy6YhViRFtN2B6FJSfBsoflXQHIdpAvGuXlSJBnpjfDKTb2k1AIdWpExu5X95S28nO0jM5LAP6XS/mIFrVRHlGvU+hPMV4NUHB+ObCw+M5pPYKf9qLXymhV63thGvsiCoYtqlcTzEO1I8PoHOrFaXkEXoKDwjtBJthtTfGJoOy1334w+nsEeHVvrll8RC0FZ+pBVrVHp8QZmbQpNQxgGpXftJL9JJfTOGf7Vpqdp04q8aip8cfg+Ks+1knrNwi0WVzU/voi0LVqenSBxOIQTNnCNKy86l6qaqPPzCMtGVqpQt3CuJser6xT7Bc5QmW3+aVwkj87fyZPnBolNr4+ROzeCGo8ju9vJbPPz4NAR9kRH8C9ZQHrGqfOF+b08PTNIdLiKODeJc4OzgtcLcnIGI19ia6GdP3/ug0hF4KqgOKCaLmrNZdt8BaVSh5k0wu+nPpCi2Ofjg72HeH/kEClVY8axyRdCGGkVUbM9I18xFqIOhIKUEncujaoISpZxwdu6VJW4UsSN2ZhJH9r8lSO99YAlFYpOALGQs72uejILGi1G4oU+leJWm1/pOsYj4TEO1QO8bnaTno7SddrBP3Wdx1kOpDz/BSuAq1i6Fbi+ZfuEEFgRSVuiSFwt4+JyuthKdSpMqtTEI/NuIMMAABGJSURBVDYWEMEAtY4Q1VbBnugINxkT6At1xl1c8q7Oy/N9TE4l2JEtrWrt+ZXGrVSgUoG5OUIvXfo9S5d7VBMJ7JCGFRbcHBhjhy+II10cHJyKRqAMYg3LFGxoIxe6D7W3CycWIndTBDOqUG0HK+bye+3fO7/+HsBRS+VUvRv/qI/wa2PIfHNctM9Vt/Dl0XsITqjXFyErKlp/D24sxPTeOJVOSd/eMT7W/jrzdoj/OPMA3312D6mXBFvGTIzRucast+U/lXWPIyWnJtpIHlQITDTnosJLKd3WQ/GTee5qO8lDwZPEFAcdH/NunScqA/wku5O5R3vpH7Fhcnatm7u2KAJXV3AXpiwsjuLKuT7CJ3Q6XqxCZu1qOV3RyIUQvcBXgHYaX1Kfl1L+qRAiCXwTGABGgA9JKddHVaqFCFMJ+LHbotRa/WS3C+qtNl0DafojWW4PjFwwS3HajnGy1oGRvfIiujVZ4XUOUKcGCLrZRJ/YiiXrHGYfwM1CiB+zCppM1BNMzcSJ56/DxIVA8ek4rVFqbX7yNzm0bcrwW71P887gDP9ldi/PTW2mbT/EvvYCwJtOfllPmqwkMu9rVLQrVK7KyC+nC7BVCHGKNbp/yu0q/3Xnd9isz9Oj6iw+31Sk4HCll8OzXbQfKKKcPIezjLnxy2lSochaavKmCAEC5ELmaXEobk3qBGckvuGZxtj6NeJqInIb+NdSyleEEBHg5YUb8uPAT6WUfyyE+H3g94F/u3JNvTLCMFA72nCSUdJ3RKm1CKo3V4lGC7yr6yxdRo5B/zRxpcKAVgf8uLhY0mHSSnCmnEK7ikV0BYKt7CIqEtjSYj8/JSnbmWKEJG3MM3sE+CkroYnC+anxCgr3hk4zvSPKU2O7abuGSoRKKETtgZ2UOzTm7rdo7cjzv/QcY5t/ilcr/fwwews/+/EuUq+6RI+krxiBr6km65jL6QIUpZRb1+r+kRr0ajlSyoW1FoatJI8evAP/iA81Pd7Iiy/j6KTLaaKiY0trzTR5M9xiifCRGaTaTsYOA+ur0/eKRi6lnAKmFn4uCiGOAd3AI8BDC2/7MvAUayy6Yhg4ySiVvhCZPQ7h9hJ/sP0JbjIm2OGrE1wypXZxnKwlHSzpkrYjzFXDKFfRB2aIAMZCSU9N6ARlBJMqc0xyBw9ymiOwwpqIhdrHW/UM70++yo+StzT6Ai7/oTd+DAbJbtMp9bv81t1P8/7IIbq0xu8/ndvBvrEB2g84BB7bf1VplPWgyWohr6HGzOV0ARbH8q2+LkLgqoKk4hBWAri450erzNoRAmd8REfcxso2yzxu/HKaLE6ZZ51dK9I0sc+OEkhFqbjGlT+wylxTjlwIMQDcBrwItC+YPMA0jdTLqiJ0H0o0DC0JykMtlNtVMrc76MkaH9h6hAF/hnsCZ8/n/hZxcXnJVJmwE/zluQcZnU3iOxokPC5peTV3TbnPqixTJEeMJHVMDBFg4alr5TSRjanqADFFsFmbZ2DrDOmP30Fw1iF8LIOoW8hqDREMYHUlqMd0slt17CDU4xI74jC0fZTNkQz9vjRjdozHy91MmAmeenUH4WGN4EThunrh10STFUZFNqZkh22qKR+BiWvvDP95XYDFsGFVdVF272Tm3hj5u2sEFRUFASgsBuZ5J0R4XBI5Z654Uayf1yRAePFX6+paUUIhGOwjuzV0fnbweuKqjVwIEQb+Efi0lLIglkR3UkopFkPEiz/3SeCTAH6CN9ban9+3T0dEwtR64szt1qj2WfyrvT9iyJhkr7+IIXTAd9HnLOnwutnPwVIfYwe6aTkKLS/N4Rw7dU0mbkub13iBIXajCZ2lrrdimrhLf3QJCp0uzeFd7cf5qwdaKA/70YtxtIqFmq9ixYNktwWodAiC96XZGpvnvanX6NUz3O4rYgiN/aafCTvBE+ntjGQTxI5pJE7UUWdy11wQak00WUX0gIUZN3D9ly7U9WasJ11KmyJU3l7i7X1n8QvtgoJoAEXHT2jGRp/KNWr9rxDrSZMrIQJ+SpsilLsUIur6Ww3pqoxcCKHTMPGvSSm/tbB5RgjRKaWcEkJ0Apfs1pZSfh74PEBUJG9omOXiQsMiHMaNRygPRpm5U6XearNj2wiDkTnuDAyTUqvo4o3HH1NavFL3M2a18LcT9zCRj2Eej+FPC7qON0q+Mjd/TW1xpctrvEAHfbSJbgB8GJiy8UdeLU1UIUCq7A2dIntzkNe6uznZ0wF1P2o5hBNySPTM0xMq84vtR2nX89zkm0QRkhfNBBknzPfStzKST1J4oY3QuCR+qoI+U7jmkTvrRZOV5lpSK/DmuthYOqzitRKPIRJxij0qd/WOcmf0LLCYXnQ4bbt8ObOXH47soDddhWJ5xZawezNN3IVIZb1dK0LXqcVU6lGJX6y/OjNXM2pFAF8EjkkpP7PkV98FPgb88cL/j61IC5egGAYiFsVpi1PuDTJ7h8LH3vcENwfGeGcgd34F68UlqRapSYcXylt5tdDLuSf7iYxI+p6dxB4db8z04trGGUspOcpLhIjQL7ad356iiylGF1+uiibQMPN7/Sb3+vcz12pyeiBKwfUzbcdp0wq8PTCHXyz9UyvMOybfrWzieKmD/ac2oc74GPxeDvfgUeDax12vN02WGweBI2Wjb0IAytW5+eV0GeXkYoGYVdFFRCLUe5JUuiUfbH2JAX0eBR0XF1PaHDW7+c7RW9GHA6jpcdx8Ydnq9izl8tfK+Ul46+ta0TTMuMCONEocrzeuJiK/D/h14LAQ4uDCtj+gYeB/L4T4BDAKfGi5Gyd0H8Kn4+waJL81iBkTmEmox1xoMxnsnOPu0Gk61BLqEqMquSaH6mHOWUkendnDRCFK/kQSY14h9ZqNf7aKLBSv+yLNk2Gac4SJsU/+GIBBbqafofND7YAcK6CJlq0SmdAYnYnxdDVIr5Zns/7GY35IKPRqBWqyTJtaJKhY6Kg4UpJ368y7Kt8v3czRUhfPPHcTRlqhZVpiFF2UdP66x0avpSarhSoErdEyMx1hrLDO1SRXLqfLKCejC0PtVuT+uQhNxQ6qOH5Jn5ZdqJypU3EtRm2VnxWGiL4QIDJhI/PFxqSvFShTcTlNxhlmVTW5SmTNJDzlYocUaq6OQiMVpa6T2QRXM2rlWd58LZiHl7c5F6IE/IhQkMm7QwR+YZbbkjM8GD/BVt80ewxnyTjwC/PgOdflB4VdvJTpY+4HPYQmXYZemMTNZHHLFXCdG5rQEhetvJMPXvJ3d/AgP5GPHpFSvvMGDvGmiJkMwbqFb7yNx/O3sDdyms36G4WMwopBeEGWxmNq4ymlsYKQzmtmN399/F7Mc2GG/nIO59Tw+Zv1RualraUmq8nW+BzTvTHqcd9VGfnldEFyUkq5Z1kbeBmkruEEFNyAQ7/mEFQa6ceydDlpdbJvqp+ubw9jT02v6ISvy2kSlBEKcn7rCh7+upC1GpGzZaxgmIo0UIW1Ik8r18u6mtmptrYgQkHMzSmqrTq1pEI9KqjdVuF9XSfYZMyx3TdFSq2iLEmfLI4FH7Ndvlu8lUOFHva9sg1jTqX9uIVvvt4YRlUz15X414Os1VAKConjKb4dvYsf9w/xcv/r3BEa4b2hCyvTKSiM21UeK93McDXFE+e2Uc77iRwxiMxKyBfXZ2Gwdcr5wOHSfXAbA+96uCSyXkdNFwhkAhytdnOr72XaVR8qKnYQZDyCKBSRa7QQ9foxckVF9rRT7Qgx9k6V1p1pHmgf4YHISbb7ZhjUG01t3EwX5sAdKSm6Ns9XB/mLAw/iH/Gx/evTkM42ijs5zgUV3ZoZt1jELRZJPm6T3B9j/q42vnHXXl6+uY9fHHoU4+fGkh+ut/Fnhx5CjAXo+1Ed31wZzhzHrdZWrQTtRkBds3JIHuuBxXHkwWiQV/K9DPmneCAwhS7AjAvMjjDGrB/WaC2DdWPkQhHU2oMU+jSUnjIPdJxhd+gcW/Q5koqDgo+8W2POEYzZMU6YXTgIXKkwXE3xwnQ/8+kIsYM+gjMuFEpNuajy1SKrNYSqEhmNYgcCjBR72Vv8jYV+uMb5ulJQzAUJHzbwpyXGVBFRKOOYZnMv07VKSMfByAqmZuNMD8SA9Td++FoQZh1fzkbLGxwwY/RqeQb19Te5ZT0jqnVeHenFlYLtfd8lKGzKm2zmLIOufDuqdHHzxWWfRHUl1o2Ro6rktvjI3WLz8R0v8XstB1GFQEFjsZnjtsZz1UF+PLeTQyf6wBUgITSq0fftWToKE7jZXGOFoLWqzrdKuOUylMsocxlaX1RpVQRCu8SfU8rGl5kr3yjdugG/2FYEx2nMbhR+Tt7SAZGpK39mHSPzBYxzKqHxLr6evod7Y2fYrI9e+YMeb5AvEn+mjSPjgxzvaOeBwBQfvOsAL23pI5ProgVQzkqczLUNZ75R1o+ROw7hKQfHr/HlwL0827vlorekSyEKhQDMGUTHFHAb6crQlAPzedxKZUUXHV6XuA5yIbpeq/zcRkU6LqEpEzD4+st38eLAAMMnOwhMaARm1t+kkCsh6xaUK0TGHJ5+eSc/iw3yzY4MFUtnvhCCUyGk+RavcnglTLPhU4bGvtIWWtQSA/40blLwT5u7UOwILYUEIl9Y1WzAujFyaduEvn+QsKoifDpcIrrslGU6F6LLpfWwpeM0FsH1Ik2PZURaddTnDhNVVeI/9IOmsaN+HOk4SNNsuqy5W6lAtUro+3m2/9QAVQVVwZCShDvfeJJdx+vVrgecQonQvrMEptp57L5byG0K8i/anuKR8DHGHkrw2rYu/NkWQtNzuNXaqqVY1o2RA2/cHM2divTYQEjbBttu9CtsBKREmubGOZ/VRrrISgUlX0GcbucJexs9/iy3Bs/RH5yn3q4xHdtEOBRE2PaqGfkVyuV5eHh4eJxHykYKd2Scwb+aYOuf2vztT97Gvz/yfnaHzvF/93+HwoCC09WCCF15GcLlYl1F5B4eHh7rHimRtoWbyaLaDuGRCGU7xt9E97I5ksaYB6XWeJJbLTwj9/Dw8LhWpMQtlXDLFbr+rorQdQgGGFM76Uwfwy2VkVezwPcy4Rm5h4eHx/UgJUhn1YcaXgohV3GkhxBijsYaSelVO+jK0sqlz6VfSpm6mh1sQE3g0rp4mtyAJrAhdfE0uZjr8pRVNXIAIcRLq1koaCVZrnPZSJrA8pyPp8nK7mc94GlyMdd7Lt6oFQ8PD48mxzNyDw8PjyZnLYz882twzJViuc5lI2kCy3M+niYru5/1gKfJxVzXuax6jtzDw8PDY3nxUiseHh4eTc6qGbkQ4t1CiBNCiNNCiN9freMuF0KIXiHEk0KIo0KI14UQv7Ow/Y+EEBNCiIML/375GvfbtLp4mlyMp8mlWQldPE2WIKVc8X80Fo48A2ymscDmIWDnahx7Gc+hE7h94ecIcBLYCfwR8LtvRV08TTxN1koXT5ML/61WRH4XcFpKOSylrAPfAB5ZpWMvC1LKKSnlKws/F4FjQPcN7rapdfE0uRhPk0uzArp4mixhtYy8Gxhb8nqcG7+41wwhxABwG/DiwqZPCSFeE0J8SQiRuIZdbRhdPE0uxtPk0iyTLp4mS/A6O68RIUQY+Efg01LKAvDnwBZgNzAF/MkaNm9N8DS5GE+TS+PpcjHLoclqGfkE0Lvkdc/CtqZCCKHTEPxrUspvAUgpZ6SUjpTSBb5A45Hvaml6XTxNLsbT5NIssy6eJktYLSM/AGwVQmwSQviADwPfXaVjLwtCCAF8ETgmpfzMku2dS972z4Aj17DbptbF0+RiPE0uzQro4mmyhFUpYyultIUQnwIep9Hb/CUp5eurcexl5D7g14HDQoiDC9v+APiIEGI3IIER4H+72h1uAF08TS7G0+TSLKsuniYX4s3s9PDw8GhyvM5ODw8PjybHM3IPDw+PJsczcg8PD48mxzNyDw8PjybHM3IPDw+PJsczcg8PD48mxzNyDw8PjybHM3IPDw+PJuf/BxsH3ikRsUcpAAAAAElFTkSuQmCC",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "def plotn(n,x):\n",
        "  fig,ax = plt.subplots(1,n)\n",
        "  for i,z in enumerate(x[0:n]):\n",
        "    ax[i].imshow(z.reshape(28,28) if z.size==28*28 else z.reshape(14,14) if z.size==14*14 else z)\n",
        "  plt.show()\n",
        "  \n",
        "plotn(5,x_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "XVXKfTiKZGzs",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "from tensorflow.keras.layers import Input, Dense, Conv2D, MaxPooling2D, UpSampling2D, Lambda\n",
        "from tensorflow.keras.models import Model\n",
        "from tensorflow.keras.losses import binary_crossentropy,mse\n",
        "\n",
        "input_img = Input(shape=(28, 28, 1))\n",
        "\n",
        "x = Conv2D(16, (3, 3), activation='relu', padding='same')(input_img)\n",
        "x = MaxPooling2D((2, 2), padding='same')(x)\n",
        "x = Conv2D(8, (3, 3), activation='relu', padding='same')(x)\n",
        "x = MaxPooling2D((2, 2), padding='same')(x)\n",
        "x = Conv2D(8, (3, 3), activation='relu', padding='same')(x)\n",
        "encoded = MaxPooling2D((2, 2), padding='same')(x)\n",
        "\n",
        "encoder = Model(input_img,encoded)\n",
        "\n",
        "input_rep = Input(shape=(4,4,8))\n",
        "\n",
        "x = Conv2D(8, (3, 3), activation='relu', padding='same')(input_rep)\n",
        "x = UpSampling2D((2, 2))(x)\n",
        "x = Conv2D(8, (3, 3), activation='relu', padding='same')(x)\n",
        "x = UpSampling2D((2, 2))(x)\n",
        "x = Conv2D(16, (3, 3), activation='relu')(x)\n",
        "x = UpSampling2D((2, 2))(x)\n",
        "decoded = Conv2D(1, (3, 3), activation='sigmoid', padding='same')(x)\n",
        "\n",
        "decoder = Model(input_rep,decoded)\n",
        "\n",
        "autoencoder = Model(input_img, decoder(encoder(input_img)))\n",
        "autoencoder.compile(optimizer='adam', loss='binary_crossentropy')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "xRVImJGBZ2kt",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "x_train = x_train.astype('float32') / 255.\n",
        "x_test = x_test.astype('float32') / 255.\n",
        "x_train = np.reshape(x_train, (len(x_train), 28, 28, 1))\n",
        "x_test = np.reshape(x_test, (len(x_test), 28, 28, 1))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 131,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "H6YD611WaAAG",
        "outputId": "3cf9f53c-8898-4bde-89b7-3670804c2373",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Train on 60000 samples, validate on 10000 samples\n",
            "Epoch 1/25\n",
            "59648/60000 [============================>.] - ETA: 0s - loss: 0.2134"
          ]
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/tensorflow/python/keras/engine/training.py:2325: UserWarning: `Model.state_updates` will be removed in a future version. This property should not be used in TensorFlow 2.0, as `updates` are applied automatically.\n",
            "  warnings.warn('`Model.state_updates` will be removed in a future version. '\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 6s 99us/sample - loss: 0.2130 - val_loss: 0.1454\n",
            "Epoch 2/25\n",
            "60000/60000 [==============================] - 5s 86us/sample - loss: 0.1353 - val_loss: 0.1258\n",
            "Epoch 3/25\n",
            "60000/60000 [==============================] - 5s 87us/sample - loss: 0.1225 - val_loss: 0.1177\n",
            "Epoch 4/25\n",
            "60000/60000 [==============================] - 5s 85us/sample - loss: 0.1163 - val_loss: 0.1126\n",
            "Epoch 5/25\n",
            "60000/60000 [==============================] - 5s 87us/sample - loss: 0.1120 - val_loss: 0.1091\n",
            "Epoch 6/25\n",
            "60000/60000 [==============================] - 5s 86us/sample - loss: 0.1093 - val_loss: 0.1070\n",
            "Epoch 7/25\n",
            "60000/60000 [==============================] - 5s 87us/sample - loss: 0.1072 - val_loss: 0.1055\n",
            "Epoch 8/25\n",
            "60000/60000 [==============================] - 5s 87us/sample - loss: 0.1057 - val_loss: 0.1041\n",
            "Epoch 9/25\n",
            "60000/60000 [==============================] - 5s 85us/sample - loss: 0.1045 - val_loss: 0.1028\n",
            "Epoch 10/25\n",
            "60000/60000 [==============================] - 5s 84us/sample - loss: 0.1035 - val_loss: 0.1022\n",
            "Epoch 11/25\n",
            "60000/60000 [==============================] - 5s 84us/sample - loss: 0.1026 - val_loss: 0.1011\n",
            "Epoch 12/25\n",
            "60000/60000 [==============================] - 5s 83us/sample - loss: 0.1018 - val_loss: 0.1003\n",
            "Epoch 13/25\n",
            "60000/60000 [==============================] - 5s 83us/sample - loss: 0.1012 - val_loss: 0.0996\n",
            "Epoch 14/25\n",
            "60000/60000 [==============================] - 5s 83us/sample - loss: 0.1005 - val_loss: 0.0991\n",
            "Epoch 15/25\n",
            "60000/60000 [==============================] - 5s 83us/sample - loss: 0.1000 - val_loss: 0.0988\n",
            "Epoch 16/25\n",
            "60000/60000 [==============================] - 5s 82us/sample - loss: 0.0995 - val_loss: 0.0981\n",
            "Epoch 17/25\n",
            "60000/60000 [==============================] - 5s 83us/sample - loss: 0.0990 - val_loss: 0.0976\n",
            "Epoch 18/25\n",
            "60000/60000 [==============================] - 5s 83us/sample - loss: 0.0986 - val_loss: 0.0974\n",
            "Epoch 19/25\n",
            "60000/60000 [==============================] - 5s 84us/sample - loss: 0.0982 - val_loss: 0.0969\n",
            "Epoch 20/25\n",
            "60000/60000 [==============================] - 5s 85us/sample - loss: 0.0978 - val_loss: 0.0970\n",
            "Epoch 21/25\n",
            "60000/60000 [==============================] - 5s 84us/sample - loss: 0.0975 - val_loss: 0.0962\n",
            "Epoch 22/25\n",
            "60000/60000 [==============================] - 5s 84us/sample - loss: 0.0971 - val_loss: 0.0960\n",
            "Epoch 23/25\n",
            "60000/60000 [==============================] - 5s 83us/sample - loss: 0.0968 - val_loss: 0.0958\n",
            "Epoch 24/25\n",
            "60000/60000 [==============================] - 5s 84us/sample - loss: 0.0966 - val_loss: 0.0953\n",
            "Epoch 25/25\n",
            "60000/60000 [==============================] - 5s 83us/sample - loss: 0.0963 - val_loss: 0.0953\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "<tensorflow.python.keras.callbacks.History at 0x7f3fa179b690>"
            ]
          },
          "execution_count": 131,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "autoencoder.fit(x_train, x_train,\n",
        "                epochs=25,\n",
        "                batch_size=128,\n",
        "                shuffle=True,\n",
        "                validation_data=(x_test, x_test))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 132,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 256
        },
        "id": "CTEBvy2FaRBF",
        "outputId": "b18d0d16-c88f-47bb-fe2e-2ba5871f0563",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/tensorflow/python/keras/engine/training.py:2325: UserWarning: `Model.state_updates` will be removed in a future version. This property should not be used in TensorFlow 2.0, as `updates` are applied automatically.\n",
            "  warnings.warn('`Model.state_updates` will be removed in a future version. '\n"
          ]
        },
        {
          "data": {
            "image/png": 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QLrSaYtfJedA00gf6mPddGxWt1RTCgfaJErJU4//7P9/Lo0fP0kWNuPQzVw5jLUjMQnNHK8h4jOyRDlJ7NX7vwS/zgDVDi2bhKMElW/JapY/F73fSc8rGvDiFfQfmWBG6gWhPUO4M8LG2F3k8OMX3y60UHAutqrZNAjHRkaSwJ0Ghz+XB6Hn2WlNLS6vJdy6xBsCobfDbZz5Cei5M5ISJmVMYS30r39mfoNrmIB9x2RkbBhozieMDaSY+lKD9FR9aExh5Zk8I+yMZHu++SFJz+c7cfqJfjhCYKOCm06uKLpFBPyIaIdiV5xejY1yx2XWcnLGljRylQDmoFUaZlm9zHacxMd12CPoNZN2BTA6EJDDhx7XecZlKIRyFcBoHsSM+LLNGUNhkXci6JcZScYJTCjO19gMTG4ppUIlL6hFFi1YgLHUkkryq8GJ5N89nd+GfVfinyqjS9ukHvhWEaWAnI5RbdcKygoag5FrkbD9iG7TEhWEifBblXa3M3adjDWTpMRaJySpy2aSfirLJug4ZV+d4tZtjhT7yZ1oIzQsiow5G3karOI1465APraxz/kg7qfAJAlLDQOOu5DTf3x9mseCjY34vMp3DnprecnM7tHgcEY9S7JQcSs7Q40sxZevMFkK0zlTQUgUcZxXhb1JD9XdT6grSEZnBEBpjdoEZx0IraI033jstauVmUbbdSGqTzSFnZgGu/BFEOn3dcXih61Tfe5Bcr8FQ6yQ7dIsXKhZvVHpxzoRp++5kI/xwg65jPVBBP/leUN0VkrKEtTRekHLhS5ceZH4szp43cvDmWZw1jm1tFoTfR3YoQG6nIKnncVCM11uYKMUQ9tYyoNUgY1FIxJh6WOc3f+or9BsL7DNrGO+4M/Kuw7FqB2+Wevnzk0cRE34G/yqLmF5AZXNLk8pc0DTaZrqxk2FeeLCPi60B+vQSLVLjN7ueYr79WX657TOMxttIvhnBv7DYMC9369xJ7uAOUgdClA+X+Xz3U8zYYX5YHiQ1HaX9xFmcQnFVDx9h6Mw8GCNzyOZfJM9RVw7/WO7jufQ+AjMCN5OF1Twg3oVtYeRXUOqaV6HrvRoJXQfDINdjkN0Nu0NzSCTHyv08NXsA37xA5QtNm6pTa23B2dVNeleQel+VgfZFgtKlquqcqmscK+9mYaSF0KiGzJbuWBOHRl2ohQX1kItP1qgql1cy/Zyeaae3uA10kQKlaTg+xZA5S4usYWBeyZJZcKuMO5Lj1T7+29jDTKcjGGcD+OcUMp3Hzeau7it2HMgV0HWN1EyMb3Qf4cdir9Fi2oSFxKfXuTc5wd/vjlBYsAiGgqhyZUsNoteiJsVOQTxapEXanHJCfHdxD0ZKb0SprOKhIywLGQpSaYNYV44d5iIuLscKfTw/PkAopRqzOtfhLW97GfnNIkSjlRKPkvtgif/r3id5wDeOJMCfXziKeraFttfLTT3dv36wj5FfUuzqGOf/6XuKLj1Pu2Yxatf4j5d+kuHJNnZ+rY51fhJnbn6zi7u5GAalTgWdVWKyxKIjeO3lIVpOCMzJKZrdyoWUKF3i+hSDhoP2jtt+1Nb4bwvv5TsX9tD7X3R2zhVgbgpVrWEXS9eamlI4c/PIfIHE8wm+kXoP/CgcbnuJgDSQSL7Q8Sy/2vYsH1G/QtsP25Dp3JYy8lyfiTya4QPd52iRJj/I7eb4PwzRcvraxuBNIQRaWxK3NYI8lOU39z/JAXOOitJ48uxdtDzlJ34qt+YzOi9zhxq5hLZWqh1h2uJpDllThKWgqmwKRR+tKRetUGssTNxsCIHQDeohnf72Ge6Nj7PTyBEWkoqymXGCnJ9uQxv3YcyncVPpdemzawqkhhYK4raEqSUc2uN5iq5F0bXwLUiCs3Uob4+BTiUECNAQV2byXu4Tf60yyPfGB1EjQczJWVhI42QyN27ELC3W7U851GZ0hvNtTLfWaJGSkLSISpOQUOiWDbq8snTeprM0Fd8OCrqjWXaYaTQhmCpHCI6Df95eVYtZaBpOIkqlK0AyPE+/kcJBsOA42FmT0FSt8ea7DpcEd6iRS5/F3EOtZAfhF7pOMWjopJwqo46Ns2gRHq+iZQpN2RKTfj+ytYVCp86/7HqFQ75xEtKkjsOEDd/N76f12z6iwyXE2BRO6TpT+e8AtFAQ++AAmaEAP3H/SzwSOcdwrYNjuT5aT9oEXrqIk91+iydc5lJd8u3CXXz53FHa/iiAbyaLOzbZ6Fq4iTqhHIfQyXl8cxHePNDDX8SO8uHwcY6sMAl7qyD9foTfR7ld8Zmul9hrTQNwcrqTXX9zAZUv4K6mW8U0mX1PhOyQ4hc7TrNTh5eqEc5Uuwhd0DFfOIG7yolFN8Mdl2RDBgLIaIRSh0D1lOk1F9DReLPWypP5uzFTGlquBpXm7BuX0QiVoXZK7YIeY5FWWUUTgqpyOVNr53ShA/+CjTGbXVWM7LbC0Km2WFTjgp3+eXr0FGk7yHQ5glFwUIViY7HlbYREogmBJgQX6kmenDxEdSSMbyKPnM803s5uoU6ISg2tWIWapOBYVJSBXGr1a0Lg89eodARxY+F1vKpbQNNA13FM6DUaMy7P121qebOxVu1qu3+EoB4SuDGbFr2AITQyTpDJahy9BG6ptG7dKnCHtciFYaL2DVDoCtL7/lF+o/9v2WOUqSqDz738aSL/6Kfv9QLi9IWmHfwrHOkl/9ksj3Sc4h4rQ0iYSCQjtsn/feZxMiMx9g7P44xPbTuTulVEOERqv05hwOYe3yhJrcZbuW4uzCXoz9e25YNOE293rfzByAcI/x9+YqlJnJm5RqTXrbZGhVj6ASkUhrCXZoo24tM/0X+Cv/zpo7S8GCdxStv0yBWhNdYldUIOd5sF/mdhkP85dYTARfO2BiGFplGNK1qSuUbkk1K8Xurj+7ODmHlvzc41RWiSWsxHuVXjcHSWu80adSVYcGuoWR+xC3X02WxTTooRuo7w+6m0aDzcdZH7QpcIicYyXWm3wsXaDtLTEQLTGqJQQq1D4p5mQ+katbBChusEReOhNlOMUMtZyFoRd7uYuN+HHbVQ5tUTMrJlH/5zI9i3sfyY8pk4QRMslxa9iE9cvSCFIRyk7qK20ru/UqDAQVFyTfJVC+E0zFgp99Yf3lIDQ8cOKjrDecKyMR8jVQ+SygeJb8Ds8DvLyE2T1F6L3C6X/YEpJJJvFnt5NT9A9KzA9/roui2Out5ovTvIH2pj8RB8puVFuvQyhvAzZpf5i8xRvjV+kP6vK/zjC41oHI/G4hzddXZ2LBKWdeYdk8mT7cSHBTKzfXKyFw60Mf2Qxp5dY40sh0t5tl11ewOQQtMoHEiQ2alzeHCYT0Vep0XTrkz5d3H5xshd7PiqQWAss6q+57VGLXWZWgsaX8ntp+RYPNJxgb9pS6C1xnGLpVtbVFoItHgU2hP07Z/mP/V/nS5NATrH5nfgDIfwL6x/o+mOMnIMnWoMVGuNmNYw7JOlbl5f7MaXVriZLGodgvXXHSFwokEKXRpOosYOvUxMNv60eddguNhGKhMkOZZFTcysOpvbtkJquKaOFarS7s/jIMi4fqyUJDDvNO0YyUpUIxK7s0pP8HJuldtoIYpGagyhaUi/j1KrRrlDsSu0QJduIZFXTLyuHPJFHx1j+S2TBlg5LtRttIpgrNpCVC/Ta6VwIg5OZwItWwT3Bq1yIRCG3oh80yRC11GtMartIXaGp9htNN5G6sqhVDMwCgJZW/8rv2OMXFgWIhyiPFjlfXuG6dVTpNwaXzt2hPirBu2n07h2ven6RKXPhwgFWTwUQf/4Ap/suERM6ljCAGDOCfHGTDdy0ofIzeJcb8GJOwhhmMiWGKXOAI/2n+ChyDCnau18L7eXtmN1gsfGcBa3z1tLsUvyiYNv8Uj4NvMxC4EWiyF8Fk53gkqLj8wHKnxq/2t8Ivr6VbvOO1VmHROnrCPs8rrMZlwNyq6jHAczB8dSPby/7RwfD50k/4CPP48dpT7SSfvL7cjrFNcxBKV2ie2HWlzhWArVUsMfqvBvWo9d2e9K7hrFhtxvd4aRS62xSngoQDhe4lBoEilcUq6OOWsQO19DpgtN2ScqfBbEIpQTgg93nudIcARDaLi4VJTNvNNGMeUnkBWNXOVb4PV2sxGGDpEQtYjGnsAsvUaKM9VOxopxfPMV7KU0D9sF2w+HAhN067f5cBISEQqiwgHKnQFKCY3Bzmk+EX2dHXoZR5k4S5HSs47JmVonoqyB7aDcrdAe50r+Jr2kmM2FSccDhKXggeB5CoMWT5n7yc22IK8T6+BYUO50cQMOoWSRkK/K3vgcbVaefiOFu5T2wEFh2xpanQ3J13NHGLkWCZF6fDf5XskTA9/nw6GTPF3cx8lCN9Fz4Ds+jpttwlVNAPvAANMPBqjdV+Bn4y+S0OpI/Jys2fxp6hGeHtlD7zcl/ukcbjOu3LIOyLYEM+9vJzsE9/pHaNFKPLO4j+MT3QyWK9fJyu0hgwFmP9xDoRcSR2d5KDnGj8WOsdOoYC2lsZ1w6kzZYf79mZ+k8GKS7hMOamp2y3Xntb6VJ21H+JsjR8k8EGB3cJaPRd/gyL4R3urvue73HCVxlUAKRVQvEZA1DliTxGSZHs3l8gpLrlLYw2H6nskgphfWPV/T9jdyqSH8fvK9ktLOGkcCl9ihw0glwYlUB4F5G2d2brNLuWoqCZPCLpvDndPsMyWSxtJtc06IV+Z7qYyHCZ2Yxl1IreuEhGZC+S1KnQK3vUK7VgAa0Sp23kA4zTnYvd4Iy0JGwhR6wRks8ys7n+XjgcupHYwr+2Vck0k7zvx4nL7X6gRGczi3Mni4QWgzaeJApSXCK309yE7F4+HjdFhTPOKfvu73iq7ibL2VotuY9WQImz49R0xKLHG1nZoZAcOjjTDWdWZbG7kMBHDvGiTTG6DrsXE+1nGcfiPFpbrkm68dJnLKIDaW2hKDMKsl26/zvz/0NHf7x65aRPnb2UNU/7qdngkbdyHVWKqsCbuO1gNl6tTiLuFIGZ9wySudfMVCljVwmrk2rA9aMsnEzw9R3OGy8+4JDsSm2W3MsVKC7TPVTv4xu4fAmE7wrVFUobDxBb4J3FQaWS7TVbEpnw3zRsddfGrgLmw/OFH7urnDRVkSOy3Rl+YN2QFQH0lztHOUzya/z8FlywULB1S1uiEBFO9q5EKIHuDLQDuNrvsvKqV+XwjRAvwPoB8YAT6llNpSI0TCsih2+8n1Sv5F90s8ERpj3rEZtuP4Rw1aT1SRi7e+OnpFlTjJK9SoAIJuBugVQ9RVjeO8CHBQCPE0G6BJLQ6/GHsDn9BY3jIaLbWQeDWHNpdeOfHR7bAUubCciipx0n1pSRM2VZN3Q+kSN+AQ9lXRBLiuoFbXkTWx5g+7G9UVYEgIMcwG3z/a8rwnclkelKVolLd/t7Q9FqZ4uMyRgTEeiZ+nx1ykRaujvWMJRUcpputxzucSWCmFPTG54vlvpEmJPBuhiVsqQakEiymsExDs7iK2s51a1KDUpnO9yEwrr4g+fQZnaYFzLdHKcP9uXhGKH28JA28/uIR7/eyra83NtMht4N8ppY4JIcLAa0s35D8DnlVK/bYQ4vPA54H/sH5FvQWWkiGpvk4mH3fo75vhHmucunL5au4wL6R2Ejvv4j87u6q+cYFgiLuIiDi2qvMyz9Ki2plmhBbaSDF3AniWTdTElA5OyERWgmjV2PVbmsrFLVeuzhctNYQUjUgf8+0mhrBMsEzKe9pJ7TGvOky9mKO1OEQgsQNrqsTJb/xnWrUdTNWHt4wml7HDFof2jPNI6zBhIRl2AzjnQ0QvgCisbYa+G9UVIK+UGtqI+0cTLlK4V5ZkA+iM5Kgd3d1YLAIodllMPwoq4GD46wjZeKgFfDX+7dAz7LWm6NAKBIRDVGpXvQFCY23PL775MB1PWrSfSV+3gXQjTTQMbFXfEE2W46YzmOddTMskGPBdP8lXrX71+q2Oi5ETZNJBMk6A5UZeiym0oZ2NJGTp9X1Gv6uRK6Wmgeml/+eFEKeBbuCTwPuWdvsz4HtsESMXmoYIBqi2+nnkwDl+OvkyfbpDHcUrmT5OTbfTN1nBHp9Y1fEt4cda6ovWhUFAhalSZp4pjvAo5xvDIsAAAA24SURBVDkBm6yJLh3sgIYWtNDKwRsY+dsrJak6oNyGfppEBAKNqJjLu4b8uAGT9KBJ/oHyO+q6gVKtZN0K5oif0FOt1FSN+frW0eQytl/jkdZhHg2eISAN8q4f/4wgNFm/MmFkrbhRXQEWl3Zbd12cFaZWtvnznO7tvbIubXZI8vnHvsE9vlEOGuqK6UtEY9o94Cjruos0A5jDfkJfff6Gb7k30sR4e1bohtYVt1RaXZ4V5aKXQRX1K/3ml7H9YCfDGKUKbLaRL0cI0Q8cBl4C2pdMHmCGRtfL5iMEsq+bS5/upNxb55da32SnnmLU1jhXb+ONlweJDAuMmZk1GUkuqyJ5MkRpoUYVS/hZquebqslPJ1/mN365k3LVpF5v4Xrvim5d4rvQh5EHvaSQNth+gWtCoc9FJN82Nqk5aJpiIDHCT7VeWPl4CJ5UXYzIFLse+gVq3/neltFEi0Sgp5N8j84ea5ourXplcHgjeGddAS4nu1lXXULjit89+UE+tvMkd7e/fGX7E4lX+f2fjVF3NFwlOBJJcdR3iYRWB8xl63hezp3Clck+y3GU4i/y/byQ3UVg+ta6pt6piZ/Q5V9tHU+5STThXvWWYuYExuh8Y1WgdeamjVwIEQL+GvhVpVROLGuOKaWUEGLFv6AQ4rPAZwF8BG6vtDdVUImdjND/gRE+1HaKD/in8AmN71eivFYcoOUtQeLVFGp24bZPZSubt3iBPdyDLgyWN1Q2W5MP+Yt86Mhfvet+abfCrw59nLOpJJlsELem4Y9UCPpq/NbQs3wqdGsRPYWiy5/8p+eIfeYJctEwPL116okIBij2RSi3CXr1NEnNQq7nirjL2My6EpyxyZ+M8EqkD6ftpSvbPxzI8vi+vwEaE1gaMz4Fl3OlXJkBKhoJsK7e723qODyzuI9Xz/fTPX/zI05b+f65ZVaoRnoR7MmpDTn9TRm5EMKgYeJ/qZT6+tLmWSFEp1JqWgjRCax4xyulvgh8ESAiWtY1bEJYFlqilXy7xWMtI7zHf4GAMJh2anzhzCdYGIsxOFKBhfRtv0K7yuUtXqCDXtpENwAmFlXVSJizUZqYGfiT7F3c7Rvj/f5bT/YVEBqfSLzBVDTObD1C1dVJGAUCssYhaxIwrrp5l7fGTtU1flDcw2w9wnA+iV1XvPwf/g5x/8O0Re4hNOliCh9Vd2M1uR4qFia9x6DcUycs65Rcyam6xnPZfURHbQIX043onjXmenXFpm7A+uviny7ScjrC2EALE3vqhIUiKs13/+I7rwOXeadKSQmG663M1GP8lwvvZWEqSvCCQXJaEbpw/b7xq451HU0u16/Nriu3zCaX4maiVgTwx8BppdTvLfvVk8AvAL+99O8316WEt4AwTdxElHKLxqOhM9xvCUBnxtEpvJKg84yLeW4a+zbjxpVSnOJVgoTpE7uvbE/SxTSjlz9uiCZWWvHNibspdVo86n/zmgGod/2+MPjJ0AKw0htKIwrGUYo6Dq5SOMtq7BuVnXx17F4W0mHEqMX8V7+C9PfT1fERYmdsfAs1krKbaXdjNbkeTtRPfpdDckeGgICKcnmpNMixhR7C53M4w5fWfObrjerKKOdalz6uqy5icp5YzWb+nlbG7QhdWp7oKrIROkqx4BjMOSG+l9vH2Xw77t+2sveFNHIx11iU4SZWVLrx/TN++eOW8JRbwVHyyoPI2WBnv5kW+UPAzwPHhRBvLG37dRoG/lUhxC8Co8Cn1qeI744wTGQkhLuzm5GPh6nvLNOuFZh2XH5/4RFemBsgftYlcj6PKt5+VEKWRWYYI0SUF9XTAAxykD72XAm1AzJsgCaxcyVm/76DPxtKcuHeBIZw0VdIFOHX6vT7FkjqeT4aGCckrx6YqSuHb5WSXKq2MV2LUnYaJu4qyel0O3OZEPWyAZW3ox6MtEZgRhArKernLpB//TUCkQ7Gjv9nJuouu2MP0c9e3uIHsIGaXMPS8nfVqEm0J8vdiSl8QjLuSP5u5iCT463sqyxc6QdeS25UV0Y5F1kKtVvX+0eVSsiUJH6mlX/58s/R0ZLjgeQI9wTHeCI0c9MP/4Kq8wezH+ZkqoOFk0n8c4KOU+W3TfwmY6ZvpMkEF9kITdYSJQHZ6COHxr1UUepykskN4WaiVn7AdcPjeWxti7M6hM+CRAup/SH+6Y8/y4PBYfp0nddrOl97+X5CF3V6X5zAHh2/vcxvS8REgg/yxIq/O8KjPKO+dkIp9cHbPtFNIF54k44XoO3Rw7yUOYDSwNWu3c/1uQR35OmJZbh/5xihd9y7JVXnL6Z/hDNT7dgpH7LU2EEoiJ+EgbNF9MnZa2ODl+nZIZ6A5ZP4llKWHBEbq8k7EZqG8FlU4zof6zvJ0eAFLKEzYwe5eL6D4CUdUVyfCVM3qisoziml7lvzk74Dt1jELRZJPB/Cl24lO9DJ1w4kODnYySeHvo4lbs7IMy48d2IvoXMmu7+1gHN6GJS65SURb6RJQIXJqdTQLR5y8xASpQO6iyEaD7GKcigpsaHdLdtiZqeMRckeaiU/INjjm6ZLz6MJk6JrYc5r+OdUIy3pNp7ZaEznaH3LQklWTOLvGpLKpRgjwRgfHvkVdOvqlpPrCMxhP4EMGHl1JSQNIDxaQZ/NogrFptRQuQrhOEhbkbN9XKy18S1l8HT6INFTOuFxZ136xrcc2TyBMR+yFkAv6Zxf6OPH3Z+iN5jm0dgZOvQsD/hylFyHl6odTNbjfHdxD4W6hRSKbNVH6JxJaNxF5L0smgDoOqVuh8GBWWJakXmnyldyd/Nato/ALQz83nYxNuxM64jTHmPmAYl/MMMDvik6tcZIdsYNEB6F6PkyqrS9b1Tn3AXCwxcbH96lhSXktTMzAVDuystdKRe7mW9a5aLqNrKumKuGKdoWTxUPcm60g31Pz6MmZnC26FTytcSZnYO5eSzAEpL2XX2k3+rmxf4eTj7SwaHWaQ51fptZx+BLUw8zPJfE990wVtZtLOVmQ9fFPFq2jOstTgI0egP69s7wGwN/S1DUGLUD/NHxh9HOBOm5tHF5e5rayGUggGyJk+0LEhjKcKRjguA7DUo1ugfuCC6brbpxP+U6dAVvfZRLYKrMaz/Yg9IUWkUQnROITL6RTKyZH1S3wvI6kisQHoug1SwWjTa+G03wWN8A9ZqOGPFjZgWxi3X0QiPcXbgKLVVAFMu4Tbqm7ZrjuiwWwxwr9/N8ehdThSj6iSCxCy76Qn7dsx5eprmNvCVO8VAXi4c0/t9DX2XIyBKSGzfBw6NJUKqR8+K1UwweN5Y2KXAV9h28dqkzO4eYXyQkBaFvaQghGqvMKwWui1Kqkbph+XdWs6blNkbZNvmZMF/3Hyb1XCfRSy79x6ZxR8Ybi1lvEE1t5MpvUU7o1KIuSa1IWEgkAhuHlFNltj6AtEE4jUrpcYfjOrgVb2GNq3CdxhuabW92KHRzUq0SOasznemg7aJDcLIC2cKGJcu6TFMbuRMPkh0Cc0eRLs0hstQaL7l1Xqm2cSzfi1FykeX6lllqysPDY/vgZLJ0/dc3QNMai2c4zoa2xC/T1EaOFCgNdK3R6WvjMO9UOVWL8wdjj3FhIsnAoo0oVnA9I/fw8FgHVpVsa41pbiN/B/NOlW8V9vA/Ju+D30mydyyLGpvCKVe8tSo9PDy2LU1t5LJQwz8bIh8I84WeD1B1dd6Y72ZhLMa+8QzMLDSmDHsm7uHhsY1paiNXZy/SNT2HME0u/uEOUIo2u0pbbQJnbgFl170Rdg8Pj21Pcxt5vYazmGp8uP56qR4eHh7bGrGRYXlCiHmgyMqp9pqRBCtfS59SKnkzB9iGmsDKunia3IYmsC118TS5llV5yoYaOYAQ4tWNSBS0EazVtWwnTWBtrsfTZH2PsxXwNLmW1V7LKrISe3h4eHhsJTwj9/Dw8GhyNsPIv7gJ51wv1upatpMmsDbX42myvsfZCniaXMuqrmXD+8g9PDw8PNYWr2vFw8PDo8nZMCMXQnxECHFWCHFeCPH5jTrvWiGE6BFCfFcIcUoIcVII8W+Wtn9BCDEphHhj6eejt3jcptXF0+RaPE1WZj108TRZhlJq3X8ADbgA7ARM4E1g/0acew2voRO4d+n/YeAcsB/4AvBrd6IuniaeJpuli6fJ1T8b1SI/CpxXSl1UStWA/w58coPOvSYopaaVUseW/p8HTgPdt3nYptbF0+RaPE1WZh108TRZxkYZeTcwvuzzBLdfuTcNIUQ/cBh4aWnT54QQbwkhviSEiN/CobaNLp4m1+JpsjJrpIunyTK8wc5bRAgRAv4a+FWlVA74Q2AXcA+NjC+/u4nF2xQ8Ta7F02RlPF2uZS002SgjnwR6ln3esbStqRBCGDQE/0ul1NcBlFKzSilHKeUCf0Tjle9maXpdPE2uxdNkZdZYF0+TZWyUkb8CDAkhBoQQJvAzwJMbdO41QQghgD8GTiulfm/Z9s5lu/04cOIWDtvUuniaXIunycqsgy6eJsvYkDS2SilbCPE54Ns0Rpu/pJQ6uRHnXkMeAn4eOC6EeGNp268DnxZC3AMoYAT4pZs94DbQxdPkWjxNVmZNdfE0uRpvZqeHh4dHk+MNdnp4eHg0OZ6Re3h4eDQ5npF7eHh4NDmekXt4eHg0OZ6Re3h4eDQ5npF7eHh4NDmekXt4eHg0OZ6Re3h4eDQ5/z87Jch2BYpZtAAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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nEMvCpD2CuT5Pz12mZHWoRRly84rhNxuwV7JVRJByifbhYZr74e+MfYcpu0tOXCwRNJqAiKY2XA6L/PnaY1S6GSIjOErziVGPaa/KEW+ZkoQccVc4zjITM3WWJ4r8n+EXuJLKMP7yCO7lxZ0b/By4VMzEKPVHS1Qf0XztyPfoa4eVoMBGJcexl9ZhvUb0YbPxAUYbxBiMAmOBq0Ic0QTGohs5iGbLMsF2pCGH+IStSousaxF6aVrdMuezJU4XpsAy4BhEGcTSiALLjjBaiEKF0RIHKwxxMHMzkCkGp+DjuCGWpbGV5tnJeR7KLFFSHUatHlmlcY1PxvbBMh+Mge4+RKFSHqpYoPvINH7RprHfojdq+KnyEnPeBgu9EoFWWKHBBDdWq+15BpWNuA6pjM+Y16KnHepRBrtjUI1uPCvb5YhtI7ZNf98wK8842IeajFpdMoOEgMiYgRGPOBeUebs3y8lLk+jmoFTdMrR9h5FMh8ulISa8OvvcdYat+MafV132j29wzrdorLuMn53C1Js7sm+P2A7iOnRn82w8JqSmWmRVn0W/zPdXDyErHtJZx/T7tz2DFsuK9S0oekOG0VSLjEQM2S2G3DbaZtBJ896fz8405CaOfEfnL2HNWwy/4THiOkgqhcmkwLYwjgUaZLOqarP/RfiBktkwupq9Yhyb/kyRIOfRK1kEWeE/PZdhdS7H1HiVg85SPKgFcrYPto7vrtrszFnFh7GZG5vNEs2MsvAFl2As4LmHTnEou8bPFF7HRfNqcz9+aJPtG0yn+/7UzQcBUUg6hc56jBWaHMssUwlzXOiOkKpqWF3HdLsfvp8djrguks+x/liKn//573MiO8+k5eKIFc/ETURHR6xHDs+3j/Li+gEKL6ZJb2i0BdoRWtMjnM8bLuwbZqjY5rnx8xxJr8TuFqvHr8+8QG/K4R/2/ia5K+NkLqahVttx14+kPFQhz8YjDl/4qdeY8apkVZ9TrXEW3pikeCbODNPt2y92EkuB69AZF2R/i0ezVxi1bGadDWrpDN9yP3QXH5mdacg3MRoTauhqjO+jghD8ALEGVVSDjI33/UmkP7CL635v27iOjdNwsNsuYc6iuezxXnqcy0ND+KkraCAy8G5tnNRFj8x6uDszFQZGXA2V8B+eoTnrYfZ1mR2u83jhMrNOhZREdLTDWxuTrC8WKTWDB7IQSKU8zPQYnak0E5krDNktlvwiG/0Mlm/iXhm7XRMR1Ogw/v4ROpOGRzKLzNmVa+6UgV/8cuRxxp/g+2uHmF8ZZnxNk9oIMJagLQFjE2agHWVYzaf4nhGWSkWeLs5z2FuO2z7YIaXJBuuPDTFCgdRZd8e1/1WlIuFkmf6Q4UB6DQvD+f4Y56ojZBeEzFp0Z5lbmz1WLIsoBblMn7zVRRHH6PrauZrNshXscEMen7kJQwhDIt+HVvsD77kzIysbFRBFKp2CdIrh/CEajSI/HD/AV3InaWqHtnGZPzXB0a/XsdZqhDtsNvGhbM7EPQ89N87Fn3VR023+wYk/56i7wozdxQJqWrEYlqm8McrYO+BeWYs13o03ro+KspB8jo0TZZr7hJ8rXeCIu8w3qw8zXy9T2gvtCgbjoXtsnMXPOJQeX+cn0vPklY3CuWrEr4Q23249zMu1fVz+4TS5ZaF4cgOp1K9ei1nPBcsiHMkT5lyWPzHKizNDqCcMx8auMGXXmbAi/t7xb/Cfp47x1+knOfhiFtPt7ahFS4K5EdYez2D2d/hE5hwvdQ7xrdXjVE4PcfTbFVS1RXibvvFNNlfnCvKa/aUKo3YDRyw6xqMSZlHRA+gjvynm7osNTBjGbhbjoUQIcuCXNCU3fnQ+F4xyujeJW1FY1SamvXMG320zyFBRpSKdIQ8z3md2pMa0U6Wo+rgiRMYwH5Y51ZvEqwqpavy0s2vdSB8RUXE6Zmdc6I3H/kwLw0o3T72RZcjXu16TTd9tr2wTzPY5XFonoyyczZxxItYixelgjOcrhzi7NkJ6VUiva6TdjbPINm9kYZxiZ9kWyo9Ir7toz6LSzwBxN00HYcqp8kh2kW8UT8BQCak1YScY8kGQs1926UwbRspNsuLTiTwW60XchkI6/fic72i/CtIpTNpDZyNmMjXyqgfARpjjcqeMusNd3gm7y5DfK0QhmTSmmKd23HDiiXM8mz+LheFP1p7ipdMHGD9liBaXd1/gb9CGU5VL+IfHqR12+eLRH/FE7hJTVpO80oBQ0Rb/fv0ZXl+bong+Inuuimnswbakt2IQ5NSlHL0nOjw9d5kj7jIRwukr49jnUtiNGno3z8YZ+MYzaeqHFH//43/OI94iGbnmsK1EEc93j/LXleO89/wB0qvC2Csd7FoPvVG9ZtSMvtaitdNFXIehrEt6w2PhRBFmwRGNJw5H7BajmVP83zOfpfXwCNn5FKyv3/8boijEsakdtjn2qfN8evgMQ8rnUneI3ukixcsGmm1Mr3dHbhWxLCgVCMbylCcb/GzpdfbbLTQeb3VmeG1xhkJt63qZP3iGfLAosZ4ZpTeewRrtcTy/Qlb51LTLmcoI3iWP9EYQF4DsJgbnpjIZTCFLZ9yjX4Zhp03e6tE3FloLbWNzORjmvdoY1Y08+Y5G+gH6fl9k24xYFpJJE+Y8ysU2B7IbpCSkbVx0zSW1LkjXv//G5y4R10FyWcKs4ZC7ypDVQ5FGYwhMxEqU5uXGAd5dGye9Es/E7WYf1e6iB37iTZeAbHZ8CgIMoDoBdtum13OoRVl6dg0AR4S80hQyPbrDebyaNyj6v7+IYyOuS5iBI7lVxu06GmhHLnZXsPs6rorWt3/zFiuePPlTBVrTLhP5FcasVryAi4m41C7jr2ZwW1s3IXjgDLnYDiqf4+JXigQPdfgfHv8OX829zZmgzOu9OTqvjnDw365Apba7CkA2g5uFAmZ6lNbBPMvPgproULS79LTD6WCMZpTmhfphzjeHWX95nOKKkFprxv1m7mDw7gXE8zAz47RmU3x28g1+pvg6FobLwTCltxRjL9dhdf1+H+ZdI+US/swQ/lDEYadBdlD40zcBFR3yjebH+fb3HiNzRTH1QhPV6kGljun3b2gS9T7PpjGodg+nYRPUPV5vzzFh1zhsd0mJhSOGJ0cX+MsnhhGdovw9dd/7sKhcFsnn6A9rfrJ4krzqxpXi/TRuPW7ZgRrMsEXxoRXdInHzsXKJy1/wcB5u8D9OvcRRR+gYoaJDfnRmHzPfgvzprbMpD5YhH8xYJZWiP6w5OL7BfnedvBLO+BO80thPah1Yq+y6dLPN4Kbks3QnsnRGFGa4TyHfQYmmoz0W/CHW/DyvrcxQr2coDPygquNDEDxwaYfiuvSH0vSLwpjboKR6NLXLWpjHbRmsantPNMnS2TS9URfJBKTkWgVnz0SsRS6XukOkVxXpNYOqtZFOLzbiQXgtOHe9ARKJi1/EIEGI8kMkSNGOPHrGAeJrx0Io2R3Ih4QpN86hvt9zBduO/dieoaQ6OBINVsyKC3m0LYjjYMIwNuZGrt3IBrpdPYlBeb8qFdFDefyRiMdGV5i2qzhi0Yx8VqI0qmGTXu0hra2LETxghlyhigX0SJHMvga/PPUy++0NOsbwT9/4CdIvZRl/dbNJ1v0ecbfJIHij8nkYLtF8ZJSl5yyi8T6fPHKektOlE3m8153k2+8dQ204jL4KpUpEen4NaXXRtTra93dcitiWIoKUCqw+5dHeH/FYaoG8hHy3e4wXqodIr0folbW4x8Yup324wNInhYf3LZFXLgqFxnAlsvhm6xG+P3+QuRc6OGuteAm3MLyWhnqz8TBoEmUiMK0OlghWu8ByN0+7GPdqUSgsESbdOuXhJn5+5JohvJ8UcvjjeUw2pKj6WGKwMIynm5wdNVhdRX6ijGqkUHrQ0dD3Byv/DAqjBi2zN2MPzWdmaE1aPPPoaf77yW/zqNtEkea73YN8r3aU/AWF/d6lOCd9i3hwDPmmb3y4RH8sw3B2nWmnSoRQiRzCSorcYoRd6xDtMmMmShDPJcpn6BcswuGAfLEbd/ATw0KvzMXWENZy7PfNXe7iVDqwVkH3fUyvPyil3iU3r3uBKIzr0B822EM98iqeRV7qD3GlVSTVi26/x8YOx88q9EjAZLrxvva0NZ3idHscv+HhVOpIPW7Te0dj4br+Iq4VXe0tsokSfXUpgB2BbRF5CmVHuKJRgCWQtXzCjCbMWQQFDwewulkkCDC2fbXFBRAHQgHJZTHZNO0xi86EsC9TYcpu4ogiJOJCf5Qz9VGcpsG0O1u6/u0DY8jFdbHKJS59ZYjWwZBfHz/NqNXkZH+KS/4I2QsWxTdXYb1yvw/1jthMLdPjQ1QfK9A4KExMVSl6PZphiovNIebfmSS1qtj3fA+n2kUWVzEfNOC7KR5wt4igXIdwOMvoiRU+NX6eWbtDTdv8f+cfwb+Y40ilht4L3Q5F6I4pnj1ynueKZwCuFgC91DnOX7/xEPlTDqxV0c3mHXd4FNvGeC5hOeTT5TPsd9avVooCLPklNtbzlJo/ZvGWbcZ4DmHWwnJ8nHiZAyzgWGaZF/bXqKYKqMDDabrkltKowGB1Qoyt8Es2GPA2fLCExlyKflnof7rJ8bFVnspepGcsroRxv5o/vfAx/DdLTM/7sYtuC8//wTDkyhpkcuToTGqGpmtMunF0/UJ/jJPNSby6iWck3d59Ptg7RFRcTZZx6ZWFIK8ZTndIWQHt0KXWSZNeUaRXDO5iDWpNdL35YBrwAWJZSMojzNgcKFR4JL1ASoTAKLrVNJkNhfT2gBEfEHmwP7PBqN0YLN0GgdGs+gWcDRuvZuJV4cPwzoy4EkwuQ1RMY2UDJuw6eRUQm8a4d0slyELdwelsXTHMHWMAI0RxXBNLhLzVZTTbplXw6A3FK2qp0EYFBqdroW2hV5K48ZXyMAo6k0K/bDg6us4TpcvkrS6BUfSw6BmHVi1DcVWwW/6WX2sPhCFX2Qzdjx+iNe3w0BMX+YWJV3Ek4vXeHP/qlU+SPe0ydbIdL1W1hY8/9xwRVDqFFPI0p1M0jodkx9s8VFhm3c/x5toktSsF9r0ekFrrwdoGutvbO321PwoiqHye8KE56odcfrX8Hs+lL1JUHu9oj/x7DsMnA6jU7veR3htEoR2Y9qqUVOyj7ZmQptGcao5Tfg9yC36cnXK7hnaQf6/SKdY+PUH9KHz+0Js86V2hpDYDqSEdHfGfLx9i9q80mcvNHZGPr6pNso5FUE1zKhhm1GoybvlM2VWeHbnAcKrNm+4UQWCx3rcxoYob7ymNnQvQWqhUXFBQ3rfObK7FT4++w6y7QU+7XNQj1KIMlSiLd9Fj5K0u9lJ1y6vD97whFzvOUumMO7SnhBOlBU54l3mzP81SUMJddihe0NgbbXQY7p4CoM2VTTwPk8/QLyiccpvRfIuy3aHiZ2l1UtgNi9RqE2ujSdTtDcrNH1Ajvonr4Jdc/IIw7VQZsSwUip5x8KqG1HI7XjZvtzPoamisuDOhIxEahTaGnhGavodXj3Ca/u2v0bqZ5prPIfkc7WnB7OvwUHaJIcvCGczG+0ZT04pOI8XsxQaq2tgRdQqm10e1etjNHO/1J/Fdi7xaw5WIMadBJ+2yVswRakUQxe2v230XJYZ8qk9khDWVR4B9xSpT6cagp4qmbTx62qESZakGWewWOOudbcmA29OGXKVSyME5unNFWl9t8NzMRb5ceIO8Cni+cYQ31qcpnobiWxuwurFzeyffBHFdlOfhPzLL2hMpGsdCvnrkHYp2l6LdYaOfhTNZ8gtgrdUxjVaclbJLzm9LuNoNMkNzxqY3alBomjpiXge81tlPZjVCltb3RLbKZhWjtg0Fq0dKIkDRNpq1KEPbd8mEcfGLiMDN0gPlWqRSLGuQh51n4RfmaB6I+OTT7/A3R37EU94iGUkDsQ/+Lb/AD9pHsJddZOXSjumzYuoNxA+YeGmIfx5+GXW0xa8eexmFwRJNX9soDJ4VMpxq0/RT1NtpAt+msZxHQsHqKNDw1sJh3rANfzV9jEK2x6MjS4x5cXV0X9vYXZDa9rhr964hHzz+BcNZOmM2n587y98afoEZu4sGFjsl1ip5ZjYiWF6PB9ouMnJiWeB59IYdWgi+DWkAABWUSURBVHOa0mSDE9lLAPjGph26eBUhVdVxxLzb3RHBpvuOKIznEOSFMBfGF6+B5TDPlX4JpxVimq3dV9V7E0RJbKAFHAmxMINAJ7S1R6Q3+/QLKBU/4W22g9404KIQFXf2E8tC8nn0cIHG0ZCHji/wt8Z+wOfTLWwyWKIITERkDItBmbebUzgNwbTb8ZPgDkD7ARKGZOdbDHl51twcb05OU3R6jLpN2qGHry1cFWErjUYIfJuoY+NULCxfkCBeJ9hpgVFC22RYL7osZdpkLZ+0FZ+rCk2c4bINT/l705APjLgMl1l+Nk17X8QTuXlGrdiIr0UuJ9+dpfS2TeZyFd3pXFt5fpegyiWiiTK1wxZHHp/nkeISs84GG1GOK70yK80chfmIzFIvzlC5w0DWhyIfyCn7YLHETrwpbs5QcynaM5rUaJfA2FwMi/zr1ed47coMc83+jjE6d41lxbnPOm7cNGo1r1YWuhJRSPVpjdtg0mQX8pheD92Njb+k02DbSC6DcR2CiTx+wWHpOYtwwudXHn+Rz+Xf5TG3ik3cMCswEUtRl+XI4/8693naz48y8mZ4Q3XofUVHGCNY88uUG11S1WHOXDxGbxh60wHiK+xWPJbPCzhtYeiSwekaUus+KoiDlmJAIo12LFZVmm7gMPZIk88U38PC0NYu3858HJQV3yS3mA815CIyC/xrYJw43vu7xph/KiJDwL8D9gMXgV8yxuyMpUAGi8uaTHzB5mcazDobZAR6Bmo6TWrJpng+QFWahHfoN+6ZDid5GZ8eIExzgDk5QmB83uJFgEdF5K/YQk1M2iMopegPGz4zcpZ93jol1aWp0/RN3PtibCPArnXjVX9uJ5D1QeP8QU0GfnlR8v7iDiX0TYe3ghfwdewPvB+afBiiBLFtQs9CF0OG8m0ihEaU43R1lO56BtWrE93Dboe3GivAERE5wxZePyKCGOjouOpSEz/mK9FkHZ9KUXDaFtl0CiE2TmIpJJsB1yEqZ4nSDs0Zj96wYurJK3x+/DS/VHyFw46HI/HK8IGJ0GjWIpfz/hhriyXm3grJXGoM+rVc0/NWmnRostWaYAzRRgWp1cm0Ongrw7T356j2HVQAdsfECyhrcJuawtlmXP28VoFIczUxXgQ7m8E7NEOQFQp2vNgyEPfrceLFJrZjSnM7M/IQ+C1jzGsikgdeHVyQvw58yxjzj0Xka8DXgL+3dYd6+4hjo4bK9MeyZOcafHzyElnVp6YVX28+zqv1OUpnNdn3VtGV6h1ftIJwhI9RkDKhCfgh32LIjLPERYYYo8Lq28C32CpNRAjHClSPuOipHo9n5impDnkVUFIdclaPVCqgX06j/DR2Losa5I1vNkCKi4i82EXjOvGjs+OApQaP2XKt/8qgB0s0PUJ3IkNnNC6AsHvgtAxWD2S1yuGVSYYWDWGvxQ8af7q9mtyObLaNFAv0h10mJjd4uLwCwFpYYO1ymcwlG+ncQde72/nMW4wVoGmMObJl1482mCjCbguvNveTUX0edy+TEhhVHT49fJbff3aU1lIG7UzidAypDZ/IUXTGHYKc0DgEYSFiZKbCTK7Jr0z+kOPuElO2oBCCQe+UN/2Ii8EIv3PyZwneLDF1Mr6+qDVvuL5upYmFQ2iCrdNkExNro+sNVBiRb3bILObimXZw7cYjfgiVetziudvFGBO7qyC+Zmx7sKjyYBMGH0VgrHiZSMu6cYK0BXyoITfGLAFLg5+bIvIuMA18Ffjc4G3/D/AddoohtyxMLo1fsNlXrvKx3AIpCekYm1frc7y9PMnUFZ9wfuEjlaR7ksYjDuzY4pAxefp0WeMKT/FZzvI2bLEmQcGlNyoMldrst6ukJMITSElARvmknJAgIzg5ByedjmfQWl9dVSl+fE7FKy1l0hjbQqddjFJgK4wlqF74vkHdnstSO2jRnosYO7xBtZmhUd3MjBkiO1pC6kvYQKZR2HZNPhTHiZ9ksooDhQoH0nFDrHqYwd2wSK0b8O9tauatxgqwMXjb1uhiNEQRdhcutcqsZwtA3JmwpDSPpy/xhYPDvJSZo7ExgtOCIOMRuUJ7WvBLmkMnFjhUWOfnyq8ya9eZtRVpcQEbSxTaRPRNwMVgjFfb+wneKjL3l22cpeqPbQN9K00crrbX3fqxYkwcG+t04ha75wezZ3UtPmA2Oz9ed3PfHB1iO5ggAANy3ZDRRhGYgWlVame4Vq5HRPYDTwAvAeMDIw+wTOx6ue+IbaNGh1n+zAjNffBzI6d4Mn2BwFhcDEZ45dUjFM4q3CsrRPdg5tU1bZrUKDKETx9P0pv/01uqibfeJT9vs3Yoz1qUpaS6OFZARgXsd9f4/NQZ/vhnskQtB2djFuULdgdUAG7ToC1o7YMobdApDcqA/f4FraOeC0EcoRcjpMbbHB5dZ392g0ezi6wHeRb6ZS61y1zYGGLjXIH8xTLhUofWao2iDOOb7dPkw1DZDL3ZEu0JxaP5K+zz1rnsD/N2c4r8RShc8OM1S7eID44VYDOiuiW6bBrR4vmQiz+Y5T884/BLhTdxRXBE2GdX+VLpTQ6k1/hW9jhN36PSzGJZmtlinXKqw08MvceEXeOIUyWvBE+cq/sPTMRJP+RSOMT/+vbfwD9VYPxHGmdhA9Ns3lap/wc1SZPb/NX2jpVB/xi4vkFj9IHfD9icYSuJG4ipOMUTwEfRNi4NnUIFbFszuts25CKSA/4Y+LvGmIZc97hgjDEictNpjIj8BvAbAKlBUGTLGPhwdTFL9RFNfq7Bp7KnOGj7vBNkmfdHKL8jjL7aiP1ddznzCk3Im/yAY5zAlvevybelmpi4S11uwWO95rAR5XAkZIiAlERMWA2+kD/J3IkN6mGGhX6ZVuhyuVWm7busr+dRtuG/evhHHE0tM+HUSEmAI/GAy4qPI5rlME9NZ2L/qnZ4LHWZR90+DtZgCSufShQxHxb4/tBR/kCeolOyOfnqf+Co8xR2tI2a3A4pj86YQ3/I8HB6kZLq8N3ecRZaJXILIalLtS3L+b0vY8XETZ8ylxqMekUuTw/RPKbIK01eWUzZMGGt86S3yk9m36FtHNaiAgrNhF0nKyGjlsZByCgPGwtrEBsJTERgIs4Fo7zZnSV6s8js9/qkzq8TLS3/+IZb91uTW3En9mAzRiTqqiHXCIGxaGuPjvZQIfGMfRvaQ9+WIRcRh9iI/xtjzJ8MNq+IyKQxZklEJoHVm/2tMeZ3gd8FKMjQlvr9leehpiZo7Stw6JErfGrkHFNWn56BP9z4BK+szZJbjLCWq+i7vGC10bzJD5hgjjGZBsDFo2/i/W65JrUGngjlk+N8bey/5NDEGr82/SJZ1SevurgS8Yi3SOQJD6fT+MaiUszR0R6XJoZwJOIL+ZOMWS0yKsTBYF3Xe8ISISU1mrpNU6doGxdHIipRRM8Y+sZwLhjnze4sP6rN8ta5GVJnLc58518wlTrKeDCJMeH2anIrlEUwPcTy5yKm9m1wxFkjMLEvM9CKTF8jfX9LilZ+3FgJCRzYel3UWo28CKmLZX6/8hxPZS/y5ewVLARHLJREWAQEBAypHpYY8mKwRMiJgyWCPSj02TTgP+ynuBhM8r/96MtwMcPE6yHepXiVqQ+6Iu5Ek80eLTvFptyUwew9XqPToT8k9Eci9qU2mLDifPnA2PEsfRv843B7WSsC/EvgXWPMP7nuV18H/hvgHw++/8ctOcI7QNJpgokizRmLvz/7XT6bXqKo0lwIezx/5QD1+SLHLjcIryzfVbtWYwzv8ApZ8uyTo1e3jzLFEvObL7dUk6hSQ+pNRl7Pgslx+rFZXiqsMuE2eDi9yKjV4JjTxRFFSjYLEmKf8GaAyhMHhQPEj8vWB9qM5sQnsCIqUYOmsdFGWNMelSjHapjnldYBfrB8gPWFEkMvK678xb8l66fYF86iw962a/JjGRQCtSc9fv3Z7/F09jyHHZuVqI82QhjF60/S9+/5Y/Ctxso8p4cHL7dUl3BlDalUKVx4kv906TjBrMVPZxZxJH6y8rDJDVwDWDeOg00iowcLNQe80H6MV2pz5L6bYfwHNWR5A12pxe6UD7m2bn39XN58uSNsyi0RAduiXzLYI132ueuMWBY906etupht7Np7OzPy54BfA94SkdcH236b2ID/oYj8t8A88Etbc4i3weaaeVNjXP6pLP0DPfY766TEIjARy1GW1rtlhk+DqrXuuudDnQ2WuUSOIi+avwLgMI+yj2NXU+2AGlupiYn7QdurNcqnbKx+im+0nibMGsyQT6nU5kuz7zLp1nk8PU9B+gxZwdXltiygJxEWQoThekV8E79+sTfN2d4EL1QOMl8t0+u6hD0begqrbeG0BbcKYxWDfv1dVhdfIyclXjCLgNl+TX4MmzOn0BNm3AoTVgOFRU3bvFzZx/pKgZFWB9Pr3fPGTrcaK/OcLgxS7bb2+hkEPfOX+rReKvOX/kP8YvmHjFpdZiyuzrhvZcD7JmQl8vlfLv0cpzdG6Z4u4VWEyXe7qPU6utO97fa3t9JkgfNsiyb3giiCSKMCwQ/iRlmB0fSMEy+wYdi2Huy3k7XyfeDHPR984d4ezkdksGp8Z67As196i8+WTnHM0aTFpWX6XA6GGX9FU3z5CtHy6l37xksywhf5hZv+7ik+yzfNH71tjPniXX3Ih2EMmIjw0gLW4hLDb2QY+U4BXc7Rnc7T2DfEH376KUbKTeozacacBse9K6Qk9qNbmEHJtqE9mG0DRAht49LTDn+48gwnlyfhrTylM5rRtQBvrY1qdDAbVUwUxYVGgzS3L6pfHFQF3idNfhyD8RGmhOPeFWbtAIVNJcpwbmEUb8FF1deI2ve++vVWYwXDaWPM0/f0A2/6ObGv3D15mbn1YebVEK89coBj3hVGVR0PG+9DMitaJuBMUOadbxxl5K2Q2dcXiJZXMUFIeIdPt7fSJGPyNEzlyB3t8H5gDCbSEIaoAHQ/9o0HxtAzNh3txZksSnZe1spOxRodpv/ILJWHHH4uH6+EDlDVXf5j6xB/sf4oXjXEtNp7bzmzzXzYfh/VaqOMIa3B8rMYO00rl+ZfjXwO7RrMZnaKAsQgVnxDM5GAkWvBpkhAC6llG7cG+csRmSs97HoXabQx3S66379qwOOd7PCWuEpQIZzzx4BVlpXPS51juBdT5C4ZGOTY7+hzuEtMr4eqNhh+t8j/8c0vo0Z7fHzfPI/mr/C3y6+REet9C0/0TMRKpLgYlvmHZ36R5eUS0+9FZC61r/Xu2WWLsNxTjI7zygdtca3Bc21be9SiTJy10u9vS1Xr7jfkIuipURZ+wsUcbvGV3ElmLAdQLITC7134FCvzQzy0VCP6CMU/uwJjMP0+Ub8P1SosCvZJGP/uwPEpKl7h5GralLrmjoJrzcIG0fWrnfA2l/sazFJ31WLU1zNIE7MCwxvtOdbDAko0f716jNHXI7KXWujNIN0eRjeb6GaT7NdXOfaXLvrRQ7z1uYf4wUMH+eLn3mZU9XEGQ6RvoKZdvtc5ynfWj+H+s2EefnslXv6u2929Y+EeEmfmxFWgm75JS4SmTrMe5rH6Jm4bvQ3tP3a1IRfbRjyP/mgafbDLI5Mr5AcZSx0TcDEcZ/XMCIWLCmnurqZYd8XgPN/XW13kWnbXoMzeXNcf5YZMg72kVRRh+j65xT5/+oNnMG58nu6azf6lNlalRRSGD0xTMRNFmF4fe71J6UwG1ff4Ve+/w3YiNjP+tBai0CJsuDhVi4NXGnFGStIG+f2EIV7V4K/b/Kg1x6y7wb9fe5pT62Nkq3FsYjvG1e425K6LGirTmHP4rRN/wYnUJUasNBpNJYIfdfYx821N7p019Nr6/T7c+8v1F5+JHhSbBcQ3NNNqYb34DsdPDgpOBhWuut0lMnp3LShyt2zGVy7Mk720QNaykN93b3zfZiWw1mg/2HVr2W45RmP6ffKXAlTg8L1jh2gGKV55MV5wOXeuPpggbf2Nb1cbclXI4+8fpTsqTDh1iqoPeFSiPn/VfogX1w/g1kKk2UZHD5DlSrgRYzBBiG624teDJ5Ad05XvfjAIghKG1zo+JrPt22cQn/LW4zqJ5tsFXlzOUjoj5JZCrHqbcJtmTLvakOuJYZafTdM91uegs86oZQhMxKmgwD979zP0L+Q5urhKVKnuif7SCXeJjjD9B9hw34rEgH8kTL+PvHmGlKU48Go27rra6WJ8n/Ae9+25FbvakANgwIRCJcrQ1CFn/Amerx8hOFMgvyBxN7tdtPJPQkLC7sIEPiYUZNDiNl6Ja3szoHavIRdB+gFe1dCrOHy3dZwz7TFeePk42UXF4T9Zgo0aYb3xYKdIJSQkbD3GYIL7tyDJ7jXkxiDdPumKJliy+KPzJ2g3U+QvKLLLGjZqRLVaMhNPSEjY8+xeQw5EC1fIV2rkPQ/+LIeErbjoxw+Imjc2tE9ISEjYi+xqQ27CMDbYrTZSrd5W68yEhISEvYaYbZy1isga0GazDd/uZ4Sbn8s+Y8zo7exgD2oCN9cl0eQuNIE9qUuiyY18JJuyrYYcQERe2ZZGQdvAvTqXvaQJ3JvzSTTZ2v3sBBJNbuSjnss2dsxNSEhISNgKEkOekJCQsMu5H4b8d+/DZ24V9+pc9pImcG/OJ9Fka/ezE0g0uZGPdC7b7iNPSEhISLi3JK6VhISEhF3OthlyEfmSiJwSkbMi8rXt+tx7hYjMisi3ReQdETkpIv/TYPvviMiiiLw++PrKHe531+qSaHIjiSY3Zyt0STS5DmPMln8Rr/V7DjgIuMAbwMPb8dn38BwmgScHP+eB08DDwO8A//ODqEuiSaLJ/dIl0eT9X9s1I/84cNYYc94Y4wN/AHx1mz77nmCMWTLGvDb4uQm8C0zf5W53tS6JJjeSaHJztkCXRJPr2C5DPg1cvu71Anc/uO8bIrIfeAJ4abDpN0XkTRH5fREp38Gu9owuiSY3kmhyc+6RLokm15EEO+8QEckBfwz8XWNMA/jnwCHgBLAE/O/38fDuC4kmN5JocnMSXW7kXmiyXYZ8EZi97vXMYNuuQkQcYsH/jTHmTwCMMSvGmMgYo4HfI37ku112vS6JJjeSaHJz7rEuiSbXsV2G/GXgiIgcEBEX+GXg69v02fcEERHgXwLvGmP+yXXbJ697288Db9/Bbne1LokmN5JocnO2QJdEk+vYlja2xphQRH4T+AZxtPn3jTEnt+Oz7yHPAb8GvCUirw+2/TbwKyJyAjDAReDv3O4O94AuiSY3kmhyc+6pLokm7yep7ExISEjY5STBzoSEhIRdTmLIExISEnY5iSFPSEhI2OUkhjwhISFhl5MY8oSEhIRdTmLIExISEnY5iSFPSEhI2OUkhjwhISFhl/P/A34p4DCd4yx/AAAAAElFTkSuQmCC",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "y_test = autoencoder.predict(x_test[0:5])\n",
        "plotn(5,x_test)\n",
        "plotn(5,y_test)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 133,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "44u_8PR7kaoY",
        "outputId": "71916b80-0821-4cd2-c481-bbbd5dac2fd4",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/tensorflow/python/keras/engine/training.py:2325: UserWarning: `Model.state_updates` will be removed in a future version. This property should not be used in TensorFlow 2.0, as `updates` are applied automatically.\n",
            "  warnings.warn('`Model.state_updates` will be removed in a future version. '\n"
          ]
        }
      ],
      "source": [
        "encoder = Model(input_img, encoded)\n",
        "encoded_imgs = encoder.predict(x_test[0:5])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 134,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 164
        },
        "id": "DJS4ZdO5oOFn",
        "outputId": "89df7031-c58b-46ae-9fc7-4ddbf5e46ef9",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plotn(5,encoded_imgs.reshape(5,-1,8))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 136,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 109
        },
        "id": "WXIys9NGz8bF",
        "outputId": "c0b2ede8-a041-4cac-ccf6-3e40817df8c5",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "6.3110805 0.0\n"
          ]
        },
        {
          "data": {
            "image/png": 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9o3Q5CRwEBpawCMsQAMsAWIZAWIbL1aqZDwAnZ1w/RZkFB0FEBoEbgd2lWQ+KyH4ReUJEOuf4M8sQMMtwiWWo0FWc4ZKr7gCoiLRS/HHqr6jqJPAtYCNwAzACfLOO5S2KZQgHyxAOlqGoVs38NLB2xvU1pXk1JSJNFP9hT6nq0wCqOqqqnqr6wHcovvWajWUIiGWwDEGxDB+qVTPfA2wSkQ0iEgXuB56p0boBEBEBHgcOquqjM+b3z7jbPcCv51iEZQiAZQAsQyAsw0fU8KjtdopHao8Bf1ur9c5Y/+0Uf9p1P7C3NG0H/gs4UJr/DNBvGSyDZbAMyyXDB5N9A9QYYxrAVXcA1BhjGpE1c2OMaQDWzI0xpgFYMzfGmAZgzdwYYxqANXNjjGkA1syNMaYBWDM3xpgG8P+v2vJSTrDNmwAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 432x288 with 7 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "print(encoded_imgs.max(),encoded_imgs.min())\n",
        "res = decoder.predict(7*np.random.rand(7,4,4,8))\n",
        "plotn(7,res)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5RQtFfjpNuI6"
      },
      "source": [
        "> **Task 1**: Try to train autoencoder with very small latent vector size, eg. 2, and plot the dots corresponding to different digits. *Hint: Use fully-connected dense layer after the convoluitonal part to reduce the vector size to the required value.*\n",
        "\n",
        "> **Task 2**: Starting from different digits, obtain their latent space representations, and see what effect adding some noise to the latent space has on the resulting digits."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xMLzTpExtPl1"
      },
      "source": [
        "## Denoising\n",
        "\n",
        "Autoencoders can be effectively used to remove noise from images. In order to train denoiser, we will start with noise-free images, and add artificial noise to them. Then, we will feed autoencoder with noisy images as input, and noise-free images as output.\n",
        "\n",
        "Let's see how this works for MNIST:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 137,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 109
        },
        "id": "uVprJu59lte0",
        "outputId": "3e9e924b-ec01-4ff3-c49a-3dd70db84db1",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "def noisify(data):\n",
        "  return np.clip(data+np.random.normal(loc=0.5,scale=0.5,size=data.shape),0.,1.)\n",
        "\n",
        "x_train_noise = noisify(x_train)\n",
        "x_test_noise = noisify(x_test)\n",
        "\n",
        "plotn(5,x_train_noise)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 141,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mlwxbuaHomTr",
        "outputId": "24c6c3be-e755-4216-815a-46561448fe7f",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Train on 60000 samples, validate on 10000 samples\n",
            "Epoch 1/25\n",
            "60000/60000 [==============================] - 6s 101us/sample - loss: 0.1576 - val_loss: 0.1566\n",
            "Epoch 2/25\n",
            "60000/60000 [==============================] - 6s 95us/sample - loss: 0.1564 - val_loss: 0.1553\n",
            "Epoch 3/25\n",
            "60000/60000 [==============================] - 6s 94us/sample - loss: 0.1555 - val_loss: 0.1539\n",
            "Epoch 4/25\n",
            "60000/60000 [==============================] - 6s 95us/sample - loss: 0.1545 - val_loss: 0.1530\n",
            "Epoch 5/25\n",
            "60000/60000 [==============================] - 6s 95us/sample - loss: 0.1538 - val_loss: 0.1517\n",
            "Epoch 6/25\n",
            "60000/60000 [==============================] - 6s 93us/sample - loss: 0.1528 - val_loss: 0.1506\n",
            "Epoch 7/25\n",
            "60000/60000 [==============================] - 6s 93us/sample - loss: 0.1521 - val_loss: 0.1499\n",
            "Epoch 8/25\n",
            "60000/60000 [==============================] - 5s 92us/sample - loss: 0.1514 - val_loss: 0.1495\n",
            "Epoch 9/25\n",
            "60000/60000 [==============================] - 6s 92us/sample - loss: 0.1508 - val_loss: 0.1487\n",
            "Epoch 10/25\n",
            "60000/60000 [==============================] - 6s 93us/sample - loss: 0.1500 - val_loss: 0.1483\n",
            "Epoch 11/25\n",
            "60000/60000 [==============================] - 6s 92us/sample - loss: 0.1495 - val_loss: 0.1484\n",
            "Epoch 12/25\n",
            "60000/60000 [==============================] - 6s 94us/sample - loss: 0.1487 - val_loss: 0.1468\n",
            "Epoch 13/25\n",
            "60000/60000 [==============================] - 6s 92us/sample - loss: 0.1482 - val_loss: 0.1467\n",
            "Epoch 14/25\n",
            "60000/60000 [==============================] - 6s 92us/sample - loss: 0.1476 - val_loss: 0.1459\n",
            "Epoch 15/25\n",
            "60000/60000 [==============================] - 6s 92us/sample - loss: 0.1469 - val_loss: 0.1450\n",
            "Epoch 16/25\n",
            "60000/60000 [==============================] - 6s 92us/sample - loss: 0.1463 - val_loss: 0.1442\n",
            "Epoch 17/25\n",
            "60000/60000 [==============================] - 6s 92us/sample - loss: 0.1457 - val_loss: 0.1441\n",
            "Epoch 18/25\n",
            "60000/60000 [==============================] - 6s 92us/sample - loss: 0.1451 - val_loss: 0.1429\n",
            "Epoch 19/25\n",
            "60000/60000 [==============================] - 6s 92us/sample - loss: 0.1445 - val_loss: 0.1425\n",
            "Epoch 20/25\n",
            "60000/60000 [==============================] - 6s 94us/sample - loss: 0.1440 - val_loss: 0.1418\n",
            "Epoch 21/25\n",
            "60000/60000 [==============================] - 6s 93us/sample - loss: 0.1435 - val_loss: 0.1423\n",
            "Epoch 22/25\n",
            "60000/60000 [==============================] - 6s 93us/sample - loss: 0.1430 - val_loss: 0.1409\n",
            "Epoch 23/25\n",
            "60000/60000 [==============================] - 6s 94us/sample - loss: 0.1426 - val_loss: 0.1405\n",
            "Epoch 24/25\n",
            "60000/60000 [==============================] - 6s 93us/sample - loss: 0.1422 - val_loss: 0.1409\n",
            "Epoch 25/25\n",
            "60000/60000 [==============================] - 6s 93us/sample - loss: 0.1418 - val_loss: 0.1398\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "<tensorflow.python.keras.callbacks.History at 0x7f3fa612c4d0>"
            ]
          },
          "execution_count": 141,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "autoencoder.fit(x_train_noise, x_train,\n",
        "                epochs=25,\n",
        "                batch_size=128,\n",
        "                shuffle=True,\n",
        "                validation_data=(x_test_noise, x_test))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 144,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 201
        },
        "id": "7kctWkcwv3kd",
        "outputId": "00bfe5d9-882b-46d3-b8b2-8310756bc9f9",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "y_test = autoencoder.predict(x_test_noise[0:5])\n",
        "plotn(5,x_test_noise)\n",
        "plotn(5,y_test)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C_u1vG1BDqVx"
      },
      "source": [
        "> **Exercise:** See how denoiser trained on MNIST digits works for different images. As an example, you can take [Fashion MNIST](https://keras.io/api/datasets/fashion_mnist/) dataset, which has the same image size. Note that denoiser works well only on the same image type that it was trained on (i.e. for the same probability distribution of input data)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fcjt-egdU6Kw"
      },
      "source": [
        "## Super-resolution\n",
        "\n",
        "Similarly to denoiser, we can train autoencoders to increase the resolution of the image. To train super-resolution network, we will start with high-resolution images, and automatically downscale them to produce network inputs. We will then feed autoencoder with small images as inputs and high-res images as outputs.\n",
        "\n",
        "Let's downscale MNIST to 14x14:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 108
        },
        "id": "JGV724C9VQ7m",
        "outputId": "d63d8ad4-55bc-431b-bc95-79f994713ad3",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x_train_lr = tf.keras.layers.AveragePooling2D()(x_train).numpy()\n",
        "x_test_lr = tf.keras.layers.AveragePooling2D()(x_test).numpy()\n",
        "plotn(5,x_train_lr)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "VXIFG2ulYuGM",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "from tensorflow.keras.layers import Input, Dense, Conv2D, MaxPooling2D, UpSampling2D, Lambda\n",
        "from tensorflow.keras.models import Model\n",
        "from tensorflow.keras.losses import binary_crossentropy,mse\n",
        "\n",
        "input_img = Input(shape=(14, 14, 1))\n",
        "\n",
        "x = Conv2D(16, (3, 3), activation='relu', padding='same')(input_img)\n",
        "x = MaxPooling2D((2, 2), padding='same')(x)\n",
        "x = Conv2D(8, (3, 3), activation='relu', padding='same')(x)\n",
        "encoded = MaxPooling2D((2, 2), padding='same')(x)\n",
        "\n",
        "encoder = Model(input_img,encoded)\n",
        "\n",
        "input_rep = Input(shape=(4,4,8))\n",
        "\n",
        "x = Conv2D(8, (3, 3), activation='relu', padding='same')(input_rep)\n",
        "x = UpSampling2D((2, 2))(x)\n",
        "x = Conv2D(8, (3, 3), activation='relu', padding='same')(x)\n",
        "x = UpSampling2D((2, 2))(x)\n",
        "x = Conv2D(16, (3, 3), activation='relu')(x)\n",
        "x = UpSampling2D((2, 2))(x)\n",
        "decoded = Conv2D(1, (3, 3), activation='sigmoid', padding='same')(x)\n",
        "\n",
        "decoder = Model(input_rep,decoded)\n",
        "\n",
        "autoencoder = Model(input_img, decoder(encoder(input_img)))\n",
        "autoencoder.compile(optimizer='adam', loss='binary_crossentropy')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tie6d1OCY2ql",
        "outputId": "0a97cea6-3fd3-41e3-c743-e332535fa779",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Epoch 1/25\n",
            "469/469 [==============================] - 6s 10ms/step - loss: 0.3413 - val_loss: 0.1519\n",
            "Epoch 2/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1457 - val_loss: 0.1292\n",
            "Epoch 3/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1273 - val_loss: 0.1202\n",
            "Epoch 4/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1189 - val_loss: 0.1142\n",
            "Epoch 5/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1148 - val_loss: 0.1107\n",
            "Epoch 6/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1115 - val_loss: 0.1083\n",
            "Epoch 7/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1093 - val_loss: 0.1063\n",
            "Epoch 8/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1071 - val_loss: 0.1046\n",
            "Epoch 9/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1060 - val_loss: 0.1037\n",
            "Epoch 10/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1048 - val_loss: 0.1026\n",
            "Epoch 11/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1039 - val_loss: 0.1019\n",
            "Epoch 12/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1030 - val_loss: 0.1012\n",
            "Epoch 13/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1024 - val_loss: 0.1004\n",
            "Epoch 14/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1017 - val_loss: 0.0999\n",
            "Epoch 15/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1010 - val_loss: 0.0993\n",
            "Epoch 16/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.1005 - val_loss: 0.0989\n",
            "Epoch 17/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.0999 - val_loss: 0.0983\n",
            "Epoch 18/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.0995 - val_loss: 0.0982\n",
            "Epoch 19/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.0990 - val_loss: 0.0975\n",
            "Epoch 20/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.0987 - val_loss: 0.0971\n",
            "Epoch 21/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.0981 - val_loss: 0.0971\n",
            "Epoch 22/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.0979 - val_loss: 0.0965\n",
            "Epoch 23/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.0977 - val_loss: 0.0959\n",
            "Epoch 24/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.0972 - val_loss: 0.0957\n",
            "Epoch 25/25\n",
            "469/469 [==============================] - 4s 9ms/step - loss: 0.0972 - val_loss: 0.0955\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "<tensorflow.python.keras.callbacks.History at 0x7f66790ada90>"
            ]
          },
          "execution_count": 8,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "autoencoder.fit(x_train_lr, x_train,\n",
        "                epochs=25,\n",
        "                batch_size=128,\n",
        "                shuffle=True,\n",
        "                validation_data=(x_test_lr, x_test))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 200
        },
        "id": "C-wLl0BiZGR4",
        "outputId": "f0104552-e056-4cbf-a238-09820839d70f",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAABbCAYAAABqBd5+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAANaklEQVR4nO3de3BU1R0H8O9v8+QVTAQiLwNqACkUhIjgo9gBEamIYx0E22msKLZqra220vFVX6MjVmfqo5apFmoHxWqnYn0TYGxVUkCR9yO8AyEJBAiRkNee/rEL5rd32WRfd/dkv58Zh/xONntPvtw9XM+991wxxoCIiOzjSXQHiIgoMhzAiYgsxQGciMhSHMCJiCzFAZyIyFIcwImILBXVAC4ik0Vki4iUicicWHXKZswkOObixEycmEl4JNLrwEUkDcBWAFcAKAewEsBMY8zG2HXPLswkOObixEycmEn40qP42TEAyowxOwBARN4AMA3AacPOlCyTjS5RbDK5dUY3NKAeLWguNcb0ZCY+ndENx3Gsqb37CjMJrqPn0hndUI86eI2XmQQ4hsMHjTE9A9ujGcD7Atjbqi4HcFGoH8hGF1wkE6LYZHKrNOU4hAPYj127/U0pnwngy2UdVhxt1RQyF2YSXEfPpdKUYzO+bN2U8pmctMS8tTtYezQDeLuIyGwAswEgG53jvTkrMBMnZhIcc3FiJt+K5iTmPgD9W9X9/G2KMWaeMabIGFOUgawoNpf8stAJJ1DfuinlMwF8uQDIbNXkyIWZcF/JQid44W3dlPKZtCWaI/CVAApFZCB8Ic8AcGNMemWpHOSiHnUAkCkimUhQJieuHqPq6hH6r9nTrF9fsKhc1c279sS0PznIBYBs7ivfYiZOOciFF14wk/aL+AjcGNMM4E4AHwHYBOBNY8yGWHXMRh7xYDBGAsAgMJNTPOIBgD3gvnIKM3HyiOfklAgzaaeo5sCNMe8DeD9GfekQekhvwGC9MaYo0X1JMkeZiQMzCZCODBhjBiW6H7bgnZhERJaK+1UoFH9lr12g6u0T5qn6laNnqXp0tr4iacboW1RdMD2GnbPUwXf1QWDus11VnbZMXe7WYex+5GJVf3DT06q+fareV7xrN8e9T26rvXGsqnMWrgjr59N768+b92it4zXe48fD71gQPAInIrIUB3AiIktxACcislRSz4HXTR/raGvsIqrutXy/qpt3Br3jtMNI+85gR9uy8c+r+tK77lF113+tVvUTr0xRdWG/qhj1zl5pZ3RX9VX9N6l65bI0N7vjmpqbx6l68U1zVX12ur7Tcd/EPFX3q9DLc7RUV8ewdy4RPaZc+7sSVS9dGN5aK7XjClRdM9i57/R78vOw3vN0eARORGQpDuBERJbiAE5EZCkO4ERElkrqk5gtNx10tJ2ZrVb7w68f+FDVTUb/Snlpdar2Gv1vVq03W9V3r7nBsc3+169vu7MuadmwxdH2sxFTVd3lcKmqPYPPU/Xy7/9R1Zcv1ic9C6EXt0oFNVefr+qFa5pUXQh9IthW3ktHqnrl439SdYvppOp606jqpb/SJzkfmqnX4t5+YbQ9dN+Bu/SJ3Dd21Ki6F8K7Wak+V48x9UNORNaxduAROBGRpTiAExFZigM4EZGlknoOvPuUMkebCajnZoxWdVq+vrHAm9dN1dKi32Hb/XrOL/D9bdBy+HDI7ze91KDqFSf6qnrIIzv0+8WmW1ZpmaHnPbNLeySoJ7Hj6eK8AaXfM/oz1WLUE3Awv7aPql+7V59fkWb9CfnnX/T5lLGP6/MpADDgwYDFoEziPmXpBf0dbX/+pb4R7tExk1Qd7ufhzBv3qvrImn5hvkP78QiciMhSHMCJiCzFAZyIyFJJPQfeHqZJX6faXB7wEOuAS5qlaJiqN49/VdVTJ810bMO2OeE9D+lF+VcM/oOqryu+U9Xp1R3jGudwpPXU50p+M+gjVS+443uqDngOtBU8Od0cbS/3f0/V49bMUHXedfqB1lkNK0Nuo2j5Hare+tMXHa+55oWrVN18oDLke8bTjmLnHPhta3+s6rMObnK8JhRz8QhVfzDkr6q+5kf69wditz/xCJyIyFIcwImILMUBnIjIUtbPgYftaX3NdOHbP9f1Br2OiA3S++prd9+ZpderGLVcz3mfV5J6c96BDk7R68OUHjuk6ubd+lpeGzUNzHe0eaAfXpD7g22qDvsKbf12SBPnMWHD+fq+g7QEzoE39HCe0fKU5kb1nrum6odePFOjH7oSzzl/HoETEVmKAzgRkaU4gBMRWarDz4F7Ruh1nu8rWKTqp2/Q6xnbds03AGyd20vVx7wZqi58Tl8rb+N6L7HWcr2e8/74df0A7T6IzUNnE6l8gnMtFG+Uf/s7ntJrZ68ar+8xmLVHryMCABmlej1tr+MV7il437n1J196SdWPTprqeE1rI8/QN5d8lK/XVB+1Sj9ToCeca/jHCo/AiYgsxQGciMhSHMCJiCzV4ebAJSNT1Ze89pWqZ//jNlUPrP4i7n2Kt43jX1H1oI/1te3nb9PX+iInR5Utx46p2pOVpWrp6pxLrZlcGLJP3RcGrKGRZCcX5g37u6rvfeH2BPUkfow42wKvA/eMHKrqshndVd37ggOq/mLoM6rO8ej19Pfeo6+vBwA5vqbNvrol80Pn2i6PXniFqpuH9HK8prXVn+1X9fMbClR95LD+vOhVd2KLR+BERJZq8whcRF4FcDWAKmPMMH9bHoBFAAYA2AVgujEm9GNhOpgNZhUOogKZyMI48Z15bzKNWIcVADBMRD5BiuWy8/NFOFK+ERnZXXEJLgcANJkGrPN+AaRoJtxPnEJlUoejSMVMItWeI/D5ACYHtM0BUGKMKQRQ4q9TSh8U4AJcqtp2YTPy0AsA1iMFc+lxbhEGTbhVte0ym5En+UCKZsL9xClUJl3RHUjBTCLV5hG4MeZTERkQ0DwN8B9iAQsALAdwXwz7FbFtc0ep+ntYpupzn1iv6kivSc2Vnqg336i2auzHaIxHGdYDLubyVaP+LXZeqefEoS/DdXikWs+DXtltlapH6ylxAMDqho9V/ex+35HUNxVVKN/UCDN8OACgenUJRg2fhbL/rQUSuK80TdTPTh2dpedlO6/V1/bGar3mRO4nAxYfcbTV3npC1f9+T58LCLxOPHDOfEWDnvO+5W96nZ2zP2v7+vlQmVRiH+DyftJySD8PVT6rOc0rg6ts0ueUzHH3Ti1GOgeeb4yp8H99AIBz1ZwU1IgGZMmpHZy5AGhsrENW5qkHCzATcD8JhplEJuqTmMYYgxA394nIbBFZJSKrmtBwupd1OKFyYSZOzCS4VMyFmbRfpAN4pYj0BgD/n1Wne6ExZp4xpsgYU5SBIP8v3oFkIgsNph5A6FxSKpPMrmho9F2myEx82rufAKmTCzOJTKQD+GIAxf6viwG8E5vu2K0n+qACu0+WzAVAj7whqKj88mTJTMD9JBhmEpn2XEb4OnwnLHuISDmAhwE8BeBNEZkFYDeA6fHsZEhjv6vK7dNfVvWkHxarWo59HZPNrjOlOIxqNKEB/zHv4RwMRQEGn7o8DMARuJTL7yfrBzHXDclTdVMX/e90VZH++U5V+vslm/QVAl2XOc+CttTWBrQcUpn8d+cTOAdDMQB9EpJJoP2X6SO1c5bcrOrCii8RD4ncT7xrNjrari/+harzH9uh6rv76JPTt3z9E1X3fUjPbJy9NvxFv0JlUoejADARiRxTwjSx2wZVv7vlMte23Z6rUJyPafeZcJr2lDBcLgraPhrjscS8td4YM9HlLiUcM3FiJk6hMik1Jag1NSmXSaR4JyYRkaU4gBMRWcr6xawaHzuq6hajb2rJqNB348bqBo1k0rKlTNWdAtaP17deADkLw3z/8LuUdAoetv8BDbGQvlQ/0PrQUv39B3Ghqntjk6oT+TCGZPXAb/Xdx2e97d6+xiNwIiJLcQAnIrIUB3AiIktZPwd+6IO+qp7wnH5gQ9Yu5wLuRESx0uXt0oRtm0fgRESW4gBORGQpDuBERJYS38qNLm1MpBq+tVN6ADjo2oYjE00fC4wx7XqWKTNxsiwTIPJ+tjsTwLpcmIlTzD8/rg7gpzYqssoYU9T2KxPH7T4yk8RvL1LMxYmZOMWjj5xCISKyFAdwIiJLJWoAn5eg7YbD7T4yk8RvL1LMxYmZOMW8jwmZAyciouhxCoWIyFKuDuAiMllEtohImYjMcXPboYjIqyJSJSLrW7XlicgnIrLN/2duHLefdLkwEydmElwic0n1TFwbwEUkDcCLAK4CMBTATBEZ6tb22zAfwOSAtjkASowxhQBK/HXMJXEu88FMAs0HMwlmPhKQCzNx9wh8DIAyY8wOY0wjgDcATHNx+6dljPkUQE1A8zQAC/xfLwBwbZw2n5S5MBMnZhJcAnNJ+UzcHMD7Atjbqi73tyWrfGNMhf/rAwDy47Qdm3JhJk7MJDg3ckn5THgSsx2M71IdXq7TCjNxYibBMRenWGXi5gC+D0D/VnU/f1uyqhSR3gDg/7MqTtuxKRdm4sRMgnMjl5TPxM0BfCWAQhEZKCKZAGYAWOzi9sO1GECx/+tiAO/EaTs25cJMnJhJcG7kwkyMMa79B2AKgK0AtgO4381tt9Gv1wFUAGiCbx5tFoAz4TtTvA3AEgB5qZQLM2EmNuSS6pnwTkwiIkvxJCYRkaU4gBMRWYoDOBGRpTiAExFZigM4EZGlOIATEVmKAzgRkaU4gBMRWer/Iuk9P3nUokwAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "y_test_lr = autoencoder.predict(x_test_lr[0:5])\n",
        "plotn(5,x_test_lr)\n",
        "plotn(5,y_test_lr)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BlnJnDwfZ_f0"
      },
      "source": [
        "> **Exercise**: Try to train super-resolution network on [CIFAR-10](https://keras.io/api/datasets/cifar10/) for 2x and 4x upscaling. Use noise as input to 4x upscaling model and observe the result."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IYKb6NwH1YOL"
      },
      "source": [
        "## Variational Auto-Encoders (VAE)\n",
        "\n",
        "Traditional autoencoders reduce the dimension of the input data somehow, figuring out the important features of input images. However, latent vectors often do not make much sense. In other words, taking MNIST dataset as an example, figuring out which digits correspond to different latent vectors is not an easy task, because close latent vectors would not necessarily correspond to the same digits. \n",
        "\n",
        "On the other hand, to train *generative* models it is better to have some understanding of the latent space. This idea leads us to **variational auto-encoder** (VAE).\n",
        "\n",
        "VAE is the autoencoder that learns to predict *statistical distribution* of the latent parameters, so-called **latent distribution**. For example, we can assume that latent vectors would be distributed as $N(\\mathrm{z\\_mean},e^{\\mathrm{z\\_log\\_sigma}})$, where $\\mathrm{z\\_mean}, \\mathrm{z\\_log\\_sigma} \\in\\mathbb{R}^d$. Encoder in VAE learns to predict those parameters, and then decoder takes a random vector from this distribution to reconstruct the object.\n",
        "\n",
        "To summarize:\n",
        "\n",
        " * From input vector, we predict `z_mean` and `z_log_sigma` (instead of predicting the standard deviation itself, we predict it's logarithm)\n",
        " * We sample a vector `sample` from the distribution $N(\\mathrm{z\\_mean},e^{\\mathrm{z\\_log\\_sigma}})$\n",
        " * Decoder tries to decode the original image using `sample` as an input vector\n",
        "\n",
        " <img src=\"images/vae.png\" width=\"50%\">"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "id": "a8bqQpG6wuJ9",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "intermediate_dim = 512\n",
        "latent_dim = 2\n",
        "batch_size = 128\n",
        "\n",
        "tf.compat.v1.disable_eager_execution()\n",
        "\n",
        "inputs = Input(shape=(784,))\n",
        "h = Dense(intermediate_dim, activation='relu')(inputs)\n",
        "z_mean = Dense(latent_dim)(h)\n",
        "z_log_sigma = Dense(latent_dim)(h)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "y6cJ93kwQkM3",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "@tf.function\n",
        "def sampling(args):\n",
        "    z_mean, z_log_sigma = args\n",
        "    bs = tf.shape(z_mean)[0]\n",
        "    epsilon = tf.random.normal(shape=(bs, latent_dim))\n",
        "    return z_mean + tf.exp(z_log_sigma) * epsilon\n",
        "\n",
        "z = Lambda(sampling)([z_mean, z_log_sigma])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "id": "Bf3UqBMXQwpQ",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "encoder = Model(inputs, [z_mean, z_log_sigma, z])\n",
        "\n",
        "latent_inputs = Input(shape=(latent_dim,))\n",
        "x = Dense(intermediate_dim, activation='relu')(latent_inputs)\n",
        "outputs = Dense(784, activation='sigmoid')(x)\n",
        "\n",
        "decoder = Model(latent_inputs, outputs)\n",
        "\n",
        "outputs = decoder(encoder(inputs)[2])\n",
        "\n",
        "vae = Model(inputs, outputs)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kY24IoGC_laa"
      },
      "source": [
        "Variational auto-encoders use complex loss function that consists of two parts:\n",
        "* **Reconstruction loss** is the loss function that shows how close reconstructed image is to the target (can be MSE). It is the same loss function as in normal autoencoders.\n",
        "* **KL loss**, which ensures that latent variable distributions stays close to normal distribution. It is based on the notion of [Kullback-Leibler divergence](https://www.countbayesie.com/blog/2017/5/9/kullback-leibler-divergence-explained) - a metric to estimate how similar two statistical distributions are."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "czXAjHUJR-BE",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "@tf.function\n",
        "def vae_loss(x1,x2):\n",
        "  reconstruction_loss = mse(x1,x2)*784\n",
        "  tmp = 1 + z_log_sigma - tf.square(z_mean) - tf.exp(z_log_sigma)\n",
        "  kl_loss = -0.5*tf.reduce_sum(tmp, axis=-1)\n",
        "  return tf.convert_to_tensor(tf.reduce_mean(reconstruction_loss + kl_loss))\n",
        "\n",
        "vae.compile(optimizer='rmsprop', loss=vae_loss)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zky-60lERlG-",
        "outputId": "baed11e4-b165-42d5-d86b-1037741554c8",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Train on 60000 samples, validate on 10000 samples\n",
            "Epoch 1/25\n",
            "59520/60000 [============================>.] - ETA: 0s - loss: 48.6396"
          ]
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/tensorflow/python/keras/engine/training.py:2325: UserWarning: `Model.state_updates` will be removed in a future version. This property should not be used in TensorFlow 2.0, as `updates` are applied automatically.\n",
            "  warnings.warn('`Model.state_updates` will be removed in a future version. '\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 4s 64us/sample - loss: 48.5874 - val_loss: 41.8877\n",
            "Epoch 2/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 41.1296 - val_loss: 40.2556\n",
            "Epoch 3/25\n",
            "60000/60000 [==============================] - 3s 56us/sample - loss: 40.0063 - val_loss: 39.3692\n",
            "Epoch 4/25\n",
            "60000/60000 [==============================] - 3s 56us/sample - loss: 39.2531 - val_loss: 38.7666\n",
            "Epoch 5/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 38.7147 - val_loss: 38.6124\n",
            "Epoch 6/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 38.2962 - val_loss: 38.1867\n",
            "Epoch 7/25\n",
            "60000/60000 [==============================] - 3s 56us/sample - loss: 37.9756 - val_loss: 37.9831\n",
            "Epoch 8/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 37.6933 - val_loss: 37.5475\n",
            "Epoch 9/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 37.4323 - val_loss: 37.2913\n",
            "Epoch 10/25\n",
            "60000/60000 [==============================] - 3s 56us/sample - loss: 37.2133 - val_loss: 37.1992\n",
            "Epoch 11/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 36.9966 - val_loss: 36.9521\n",
            "Epoch 12/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 36.8204 - val_loss: 36.8431\n",
            "Epoch 13/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 36.6490 - val_loss: 36.6979\n",
            "Epoch 14/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 36.5023 - val_loss: 36.6661\n",
            "Epoch 15/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 36.3456 - val_loss: 36.4957\n",
            "Epoch 16/25\n",
            "60000/60000 [==============================] - 3s 56us/sample - loss: 36.2266 - val_loss: 36.6669\n",
            "Epoch 17/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 36.1045 - val_loss: 36.4855\n",
            "Epoch 18/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 35.9922 - val_loss: 36.4150\n",
            "Epoch 19/25\n",
            "60000/60000 [==============================] - 3s 56us/sample - loss: 35.8968 - val_loss: 36.1196\n",
            "Epoch 20/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 35.7991 - val_loss: 36.0708\n",
            "Epoch 21/25\n",
            "60000/60000 [==============================] - 3s 56us/sample - loss: 35.7129 - val_loss: 36.1686\n",
            "Epoch 22/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 35.6214 - val_loss: 36.1080\n",
            "Epoch 23/25\n",
            "60000/60000 [==============================] - 3s 57us/sample - loss: 35.5357 - val_loss: 36.2309\n",
            "Epoch 24/25\n",
            "60000/60000 [==============================] - 3s 56us/sample - loss: 35.4528 - val_loss: 36.1416\n",
            "Epoch 25/25\n",
            "60000/60000 [==============================] - 3s 56us/sample - loss: 35.3650 - val_loss: 35.7258\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "<tensorflow.python.keras.callbacks.History at 0x7f0e00233890>"
            ]
          },
          "execution_count": 25,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x_train_flat = x_train.reshape((len(x_train), np.prod(x_train.shape[1:])))\n",
        "x_test_flat = x_test.reshape((len(x_test), np.prod(x_test.shape[1:])))\n",
        "\n",
        "vae.fit(x_train_flat, x_train_flat,\n",
        "        shuffle=True,\n",
        "        epochs=25,\n",
        "        batch_size=batch_size,\n",
        "        validation_data=(x_test_flat, x_test_flat))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 256
        },
        "id": "YF8hHAZVR5x_",
        "outputId": "146edef1-676d-4592-8b9f-250ff4b98fa6",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/tensorflow/python/keras/engine/training.py:2325: UserWarning: `Model.state_updates` will be removed in a future version. This property should not be used in TensorFlow 2.0, as `updates` are applied automatically.\n",
            "  warnings.warn('`Model.state_updates` will be removed in a future version. '\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "y_test = vae.predict(x_test_flat[0:5])\n",
        "plotn(5,x_test_flat)\n",
        "plotn(5,y_test)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 433
        },
        "id": "jZ0PzYmInDi5",
        "outputId": "b114fa04-ba23-47e3-b63e-1e3eac248463",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/tensorflow/python/keras/engine/training.py:2325: UserWarning: `Model.state_updates` will be removed in a future version. This property should not be used in TensorFlow 2.0, as `updates` are applied automatically.\n",
            "  warnings.warn('`Model.state_updates` will be removed in a future version. '\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x_test_encoded = encoder.predict(x_test_flat)[0]\n",
        "plt.figure(figsize=(6, 6))\n",
        "plt.scatter(x_test_encoded[:, 0], x_test_encoded[:, 1], c=y_testclass)\n",
        "plt.colorbar()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        },
        "id": "AZQfTelyOigw",
        "outputId": "3c0fc864-e3e5-4b57-d84f-572358f2e61b",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/tensorflow/python/keras/engine/training.py:2325: UserWarning: `Model.state_updates` will be removed in a future version. This property should not be used in TensorFlow 2.0, as `updates` are applied automatically.\n",
            "  warnings.warn('`Model.state_updates` will be removed in a future version. '\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 100 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "def plotsample(n):\n",
        "  dx = np.linspace(-1,1,n)\n",
        "  dy = np.linspace(-1,1,n)\n",
        "  fig,ax = plt.subplots(n,n)\n",
        "  for i,xi in enumerate(dx):\n",
        "    for j,xj in enumerate(dy):\n",
        "      res = decoder.predict(np.array([xi,xj]).reshape(-1,2))[0]\n",
        "      ax[i,j].imshow(res.reshape(28,28))\n",
        "      ax[i,j].axis('off')\n",
        "  plt.show()\n",
        "  \n",
        "plotsample(10)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WiKTnnIQUgdP"
      },
      "source": [
        "> **Task**: In our sample, we have trained fully-connected VAE. Now take the CNN from traditional auto-encoder above and create CNN-based VAE."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DhJLlh30Brpb"
      },
      "source": [
        "## Additional Materials\n",
        "\n",
        "* [Blog post on NeuroHive](https://neurohive.io/ru/osnovy-data-science/variacionnyj-avtojenkoder-vae/)\n",
        "* [Variational Autoencoders Explained](https://kvfrans.com/variational-autoencoders-explained/)"
      ]
    }
  ],
  "metadata": {
    "accelerator": "GPU",
    "colab": {
      "collapsed_sections": [],
      "name": "Autoencoders.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
